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Общий знаменатель sin(pi/3-a)+cos(pi/6+a)

Выражение, которое надо упростить:

Решение

Вы ввели [src]
   /pi    \      /pi    \
sin|-- - a| + cos|-- + a|
   \3     /      \6     /
$$\sin{\left(- a + \frac{\pi}{3} \right)} + \cos{\left(a + \frac{\pi}{6} \right)}$$
sin(pi/3 - a) + cos(pi/6 + a)
Общее упрощение [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
2*cos(a + pi/6)
Разложение дроби [src]
2*cos(a + pi/6)
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
     /    pi\
2*cos|a + --|
     \    6 /
Рациональный знаменатель [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
     /pi + 6*a\
2*cos|--------|
     \   6    /
$$2 \cos{\left(\frac{6 a + \pi}{6} \right)}$$
2*cos((pi + 6*a)/6)
Собрать выражение [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
2*cos(a + pi/6)
Раскрыть выражение [src]
            ___       
-sin(a) + \/ 3 *cos(a)
$$- \sin{\left(a \right)} + \sqrt{3} \cos{\left(a \right)}$$
-sin(a) + sqrt(3)*cos(a)
Объединение рациональных выражений [src]
   /pi + 6*a\      /pi - 3*a\
cos|--------| + sin|--------|
   \   6    /      \   3    /
$$\sin{\left(\frac{- 3 a + \pi}{3} \right)} + \cos{\left(\frac{6 a + \pi}{6} \right)}$$
cos((pi + 6*a)/6) + sin((pi - 3*a)/3)
Комбинаторика [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
2*cos(a + pi/6)
Степени [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
   /    pi\      /     pi\     /     /    pi\      /     pi\\
 I*|a + --|    I*|-a - --|     |   I*|a - --|    I*|-a + --||
   \    6 /      \     6 /     |     \    3 /      \     3 /|
e             e              I*\- e           + e           /
----------- + ------------ - --------------------------------
     2             2                        2                
$$- \frac{i \left(e^{i \left(- a + \frac{\pi}{3}\right)} - e^{i \left(a - \frac{\pi}{3}\right)}\right)}{2} + \frac{e^{i \left(- a - \frac{\pi}{6}\right)}}{2} + \frac{e^{i \left(a + \frac{\pi}{6}\right)}}{2}$$
exp(i*(a + pi/6))/2 + exp(i*(-a - pi/6))/2 - i*(-exp(i*(a - pi/3)) + exp(i*(-a + pi/3)))/2
Тригонометрическая часть [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
     /    2*pi\
2*sin|a + ----|
     \     3  /
$$2 \sin{\left(a + \frac{2 \pi}{3} \right)}$$
     2     
-----------
   /    pi\
sec|a + --|
   \    6 /
$$\frac{2}{\sec{\left(a + \frac{\pi}{6} \right)}}$$
     2      
------------
   /     pi\
csc|-a + --|
   \     3 /
$$\frac{2}{\csc{\left(- a + \frac{\pi}{3} \right)}}$$
            ___       
-sin(a) + \/ 3 *cos(a)
$$- \sin{\left(a \right)} + \sqrt{3} \cos{\left(a \right)}$$
      /a   pi\  
 4*tan|- + --|  
      \2   3 /  
----------------
       2/a   pi\
1 + tan |- + --|
        \2   3 /
$$\frac{4 \tan{\left(\frac{a}{2} + \frac{\pi}{3} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{3} \right)} + 1}$$
  /        2/a   pi\\
2*|-1 + cot |- + --||
  \         \2   12//
---------------------
          2/a   pi\  
   1 + cot |- + --|  
           \2   12/  
$$\frac{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} - 1\right)}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1}$$
  /       2/a   pi\\
2*|1 - tan |- + --||
  \        \2   12//
--------------------
         2/a   pi\  
  1 + tan |- + --|  
          \2   12/  
$$\frac{2 \cdot \left(- \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1\right)}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1}$$
  /         1      \
2*|1 - ------------|
  |       2/a   pi\|
  |    cot |- + --||
  \        \2   12//
--------------------
           1        
  1 + ------------  
         2/a   pi\  
      cot |- + --|  
          \2   12/  
$$\frac{2 \cdot \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}\right)}{1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}$$
  //                 /    pi\             \
  ||     1       for |a + --| mod 2*pi = 0|
  ||                 \    6 /             |
2*|<                                      |
  ||   /    pi\                           |
  ||cos|a + --|          otherwise        |
  \\   \    6 /                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\cos{\left(a + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases}\right)$$
  //                 /    2*pi\           \
  ||     0       for |a + ----| mod pi = 0|
  ||                 \     3  /           |
2*|<                                      |
  ||   /    pi\                           |
  ||cos|a + --|          otherwise        |
  \\   \    6 /                           /
$$2 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{2 \pi}{3}\right) \bmod \pi = 0 \\\cos{\left(a + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases}\right)$$
  //                   /    pi\             \
  ||      1        for |a + --| mod 2*pi = 0|
  ||                   \    6 /             |
2*|<                                        |
  ||   /    2*pi\                           |
  ||sin|a + ----|          otherwise        |
  \\   \     3  /                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\sin{\left(a + \frac{2 \pi}{3} \right)} & \text{otherwise} \end{cases}\right)$$
  //                 /    pi\             \
  ||     1       for |a + --| mod 2*pi = 0|
  ||                 \    6 /             |
  ||                                      |
2*|<     1                                |
  ||-----------          otherwise        |
  ||   /    pi\                           |
  ||sec|a + --|                           |
  \\   \    6 /                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(a + \frac{\pi}{6} \right)}} & \text{otherwise} \end{cases}\right)$$
  //                  /    pi\             \
  ||     1        for |a + --| mod 2*pi = 0|
  ||                  \    6 /             |
  ||                                       |
2*|<     1                                 |
  ||------------          otherwise        |
  ||   /     pi\                           |
  ||csc|-a + --|                           |
  \\   \     3 /                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- a + \frac{\pi}{3} \right)}} & \text{otherwise} \end{cases}\right)$$
  //                      /    2*pi\           \
  ||       0          for |a + ----| mod pi = 0|
  ||                      \     3  /           |
  ||                                           |
  ||      /a   pi\                             |
2*|< 2*cot|- + --|                             |
  ||      \2   3 /                             |
  ||----------------          otherwise        |
  ||       2/a   pi\                           |
  ||1 + cot |- + --|                           |
  \\        \2   3 /                           /
$$2 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{2 \pi}{3}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{3} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{3} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
  /         4/a   pi\\
  |    4*sin |- + --||
  |          \2   12/|
2*|1 - --------------|
  |        2/    pi\ |
  |     sin |a + --| |
  \         \    6 / /
----------------------
           4/a   pi\  
      4*sin |- + --|  
            \2   12/  
  1 + --------------  
          2/    pi\   
       sin |a + --|   
           \    6 /   
$$\frac{2 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(a + \frac{\pi}{6} \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(a + \frac{\pi}{6} \right)}} + 1}$$
  //                       /    pi\             \
  ||        1          for |a + --| mod 2*pi = 0|
  ||                       \    6 /             |
  ||                                            |
  ||        2/a   pi\                           |
2*|<-1 + cot |- + --|                           |
  ||         \2   12/                           |
  ||-----------------          otherwise        |
  ||        2/a   pi\                           |
  || 1 + cot |- + --|                           |
  \\         \2   12/                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
  /          2/a   pi\\
  |     2*sin |- + --||
  |           \2   12/|
2*|1 - ---------------|
  |           /    pi\|
  |    1 + cos|a + --||
  \           \    6 //
-----------------------
            2/a   pi\  
       2*sin |- + --|  
             \2   12/  
  1 + ---------------  
             /    pi\  
      1 + cos|a + --|  
             \    6 /  
$$\frac{2 \cdot \left(- \frac{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos{\left(a + \frac{\pi}{6} \right)} + 1} + 1\right)}{\frac{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos{\left(a + \frac{\pi}{6} \right)} + 1} + 1}$$
  //                      /    pi\             \
  ||       1          for |a + --| mod 2*pi = 0|
  ||                      \    6 /             |
  ||                                           |
  ||       2/a   pi\                           |
2*|<1 - tan |- + --|                           |
  ||        \2   12/                           |
  ||----------------          otherwise        |
  ||       2/a   pi\                           |
  ||1 + tan |- + --|                           |
  \\        \2   12/                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
  /       2/a   5*pi\\
  |    cos |- - ----||
  |        \2    12 /|
2*|1 - --------------|
  |        2/a   pi\ |
  |     cos |- + --| |
  \         \2   12/ /
----------------------
         2/a   5*pi\  
      cos |- - ----|  
          \2    12 /  
  1 + --------------  
          2/a   pi\   
       cos |- + --|   
           \2   12/   
$$\frac{2 \left(- \frac{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1\right)}{\frac{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1}$$
  //                       /    pi\             \
  ||        1          for |a + --| mod 2*pi = 0|
  ||                       \    6 /             |
  ||                                            |
  ||          1                                 |
  ||-1 + ------------                           |
  ||        2/a   pi\                           |
2*|<     tan |- + --|                           |
  ||         \2   12/                           |
  ||-----------------          otherwise        |
  ||          1                                 |
  || 1 + ------------                           |
  ||        2/a   pi\                           |
  ||     tan |- + --|                           |
  \\         \2   12/                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
  /       2/  a   5*pi\\
  |    csc |- - + ----||
  |        \  2    12 /|
2*|1 - ----------------|
  |         2/a   pi\  |
  |      csc |- + --|  |
  \          \2   12/  /
------------------------
         2/  a   5*pi\  
      csc |- - + ----|  
          \  2    12 /  
  1 + ----------------  
           2/a   pi\    
        csc |- + --|    
            \2   12/    
$$\frac{2 \left(- \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1\right)}{\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1}$$
  /        2/a   pi\ \
  |     sec |- + --| |
  |         \2   12/ |
2*|1 - --------------|
  |       2/a   5*pi\|
  |    sec |- - ----||
  \        \2    12 //
----------------------
          2/a   pi\   
       sec |- + --|   
           \2   12/   
  1 + --------------  
         2/a   5*pi\  
      sec |- - ----|  
          \2    12 /  
$$\frac{2 \cdot \left(1 - \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}\right)}{1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}}$$
  /                  2               \
2*|1 - ------------------------------|
  |    /       /    pi\\    2/a   pi\|
  |    |1 + cos|a + --||*csc |- + --||
  \    \       \    6 //     \2   12//
--------------------------------------
                    2                 
  1 + ------------------------------  
      /       /    pi\\    2/a   pi\  
      |1 + cos|a + --||*csc |- + --|  
      \       \    6 //     \2   12/  
$$\frac{2 \cdot \left(1 - \frac{2}{\left(\cos{\left(a + \frac{\pi}{6} \right)} + 1\right) \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}\right)}{1 + \frac{2}{\left(\cos{\left(a + \frac{\pi}{6} \right)} + 1\right) \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}$$
  //                                             /    pi\             \
  ||                   1                     for |a + --| mod 2*pi = 0|
  ||                                             \    6 /             |
  ||                                                                  |
  ||/                 /    pi\                                        |
2*|<|     1       for |a + --| mod 2*pi = 0                           |
  |||                 \    6 /                                        |
  ||<                                                otherwise        |
  |||   /    pi\                                                      |
  |||cos|a + --|          otherwise                                   |
  \\\   \    6 /                                                      /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\cos{\left(a + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
  //                         /    pi\             \
  ||         1           for |a + --| mod 2*pi = 0|
  ||                         \    6 /             |
  ||                                              |
  ||         2/    pi\                            |
  ||      sin |a + --|                            |
  ||          \    6 /                            |
  ||-1 + --------------                           |
  ||          4/a   pi\                           |
2*|<     4*sin |- + --|                           |
  ||           \2   12/                           |
  ||-------------------          otherwise        |
  ||         2/    pi\                            |
  ||      sin |a + --|                            |
  ||          \    6 /                            |
  || 1 + --------------                           |
  ||          4/a   pi\                           |
  ||     4*sin |- + --|                           |
  \\           \2   12/                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(a + \frac{\pi}{6} \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}{1 + \frac{\sin^{2}{\left(a + \frac{\pi}{6} \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
  //                          /    pi\             \
  ||         1            for |a + --| mod 2*pi = 0|
  ||                          \    6 /             |
  ||                                               |
  ||           2/a   pi\                           |
  ||      2*cos |- + --|                           |
  ||            \2   12/                           |
  ||-1 + ---------------                           |
  ||            /    pi\                           |
2*|<     1 - cos|a + --|                           |
  ||            \    6 /                           |
  ||--------------------          otherwise        |
  ||          2/a   pi\                            |
  ||     2*cos |- + --|                            |
  ||           \2   12/                            |
  ||1 + ---------------                            |
  ||           /    pi\                            |
  ||    1 - cos|a + --|                            |
  \\           \    6 /                            /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\frac{2 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{- \cos{\left(a + \frac{\pi}{6} \right)} + 1} - 1}{\frac{2 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{- \cos{\left(a + \frac{\pi}{6} \right)} + 1} + 1} & \text{otherwise} \end{cases}\right)$$
  //                                                   /    pi\             \
  ||                      1                        for |a + --| mod 2*pi = 0|
  ||                                                   \    6 /             |
  ||                                                                        |
  ||/                       /    pi\                                        |
  |||        1          for |a + --| mod 2*pi = 0                           |
  |||                       \    6 /                                        |
2*|<|                                                                       |
  |||        2/a   pi\                                                      |
  ||<-1 + cot |- + --|                                     otherwise        |
  |||         \2   12/                                                      |
  |||-----------------          otherwise                                   |
  |||        2/a   pi\                                                      |
  ||| 1 + cot |- + --|                                                      |
  \\\         \2   12/                                                      /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
  //                         /    pi\             \
  ||         1           for |a + --| mod 2*pi = 0|
  ||                         \    6 /             |
  ||                                              |
  ||        2/a   5*pi\                           |
  ||     sec |- - ----|                           |
  ||         \2    12 /                           |
  ||-1 + --------------                           |
  ||         2/a   pi\                            |
2*|<      sec |- + --|                            |
  ||          \2   12/                            |
  ||-------------------          otherwise        |
  ||        2/a   5*pi\                           |
  ||     sec |- - ----|                           |
  ||         \2    12 /                           |
  || 1 + --------------                           |
  ||         2/a   pi\                            |
  ||      sec |- + --|                            |
  \\          \2   12/                            /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\frac{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} - 1}{\frac{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
  //                         /    pi\             \
  ||         1           for |a + --| mod 2*pi = 0|
  ||                         \    6 /             |
  ||                                              |
  ||         2/a   pi\                            |
  ||      cos |- + --|                            |
  ||          \2   12/                            |
  ||-1 + --------------                           |
  ||        2/a   5*pi\                           |
2*|<     cos |- - ----|                           |
  ||         \2    12 /                           |
  ||-------------------          otherwise        |
  ||         2/a   pi\                            |
  ||      cos |- + --|                            |
  ||          \2   12/                            |
  || 1 + --------------                           |
  ||        2/a   5*pi\                           |
  ||     cos |- - ----|                           |
  \\         \2    12 /                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
  //                           /    pi\             \
  ||          1            for |a + --| mod 2*pi = 0|
  ||                           \    6 /             |
  ||                                                |
  ||          2/a   pi\                             |
  ||       csc |- + --|                             |
  ||           \2   12/                             |
  ||-1 + ----------------                           |
  ||        2/  a   5*pi\                           |
2*|<     csc |- - + ----|                           |
  ||         \  2    12 /                           |
  ||---------------------          otherwise        |
  ||          2/a   pi\                             |
  ||       csc |- + --|                             |
  ||           \2   12/                             |
  || 1 + ----------------                           |
  ||        2/  a   5*pi\                           |
  ||     csc |- - + ----|                           |
  \\         \  2    12 /                           /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}}{1 + \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
2*Piecewise((1, Mod(a + pi/6 = 2*pi, 0)), ((-1 + csc(a/2 + pi/12)^2/csc(-a/2 + 5*pi/12)^2)/(1 + csc(a/2 + pi/12)^2/csc(-a/2 + 5*pi/12)^2), True))
Общий знаменатель [src]
     /    pi\
2*cos|a + --|
     \    6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
2*cos(a + pi/6)
Численный ответ [src]
cos(pi/6 + a) + sin(pi/3 - a)
cos(pi/6 + a) + sin(pi/3 - a)