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cos(20)*l если l=-4

Выражение, которое надо упростить:

Решение

Вы ввели [src]
cos(20)*l
$$l \cos{\left(20 \right)}$$
cos(20)*l
Разложение на множители [src]
1*(l + 0)
$$1 \left(l + 0\right)$$
1*(l + 0)
Подстановка условия [src]
cos(20)*l при l = -4
подставляем
cos(20)*l
$$l \cos{\left(20 \right)}$$
l*cos(20)
$$l \cos{\left(20 \right)}$$
переменные
l = -4
$$l = -4$$
(-4)*cos(20)
$$(-4) \cos{\left(20 \right)}$$
-4*cos(20)
$$- 4 \cos{\left(20 \right)}$$
-4*cos(20)
Степени [src]
  / -20*I    20*I\
  |e        e    |
l*|------ + -----|
  \  2        2  /
$$l \left(\frac{e^{- 20 i}}{2} + \frac{e^{20 i}}{2}\right)$$
l*(exp(-20*i)/2 + exp(20*i)/2)
Численный ответ [src]
0.408082061813392*l
0.408082061813392*l
Тригонометрическая часть [src]
   l   
-------
sec(20)
$$\frac{l}{\sec{\left(20 \right)}}$$
     /     pi\
l*sin|20 + --|
     \     2 /
$$l \sin{\left(\frac{\pi}{2} + 20 \right)}$$
      l      
-------------
   /      pi\
csc|-20 + --|
   \      2 /
$$\frac{l}{\csc{\left(-20 + \frac{\pi}{2} \right)}}$$
                   /     pi\
l*(1 + sin(20))*cot|10 + --|
                   \     4 /
$$l \left(\sin{\left(20 \right)} + 1\right) \cot{\left(\frac{\pi}{4} + 10 \right)}$$
  /        2    \
l*\-1 + cot (10)/
-----------------
          2      
   1 + cot (10)  
$$\frac{l \left(-1 + \cot^{2}{\left(10 \right)}\right)}{1 + \cot^{2}{\left(10 \right)}}$$
  /       2    \
l*\1 - tan (10)/
----------------
         2      
  1 + tan (10)  
$$\frac{l \left(- \tan^{2}{\left(10 \right)} + 1\right)}{\tan^{2}{\left(10 \right)} + 1}$$
        /     pi\
 2*l*tan|10 + --|
        \     4 /
-----------------
       2/     pi\
1 + tan |10 + --|
        \     4 /
$$\frac{2 l \tan{\left(\frac{\pi}{4} + 10 \right)}}{1 + \tan^{2}{\left(\frac{\pi}{4} + 10 \right)}}$$
        /     pi\
 2*l*cot|10 + --|
        \     4 /
-----------------
       2/     pi\
1 + cot |10 + --|
        \     4 /
$$\frac{2 l \cot{\left(\frac{\pi}{4} + 10 \right)}}{\cot^{2}{\left(\frac{\pi}{4} + 10 \right)} + 1}$$
  /        1    \
l*|-1 + --------|
  |        2    |
  \     tan (10)/
-----------------
          1      
   1 + --------  
          2      
       tan (10)  
$$\frac{l \left(-1 + \frac{1}{\tan^{2}{\left(10 \right)}}\right)}{1 + \frac{1}{\tan^{2}{\left(10 \right)}}}$$
  /       1    \
l*|1 - --------|
  |       2    |
  \    cot (10)/
----------------
         1      
  1 + --------  
         2      
      cot (10)  
$$\frac{l \left(- \frac{1}{\cot^{2}{\left(10 \right)}} + 1\right)}{\frac{1}{\cot^{2}{\left(10 \right)}} + 1}$$
2*l*(-1 - cos(40) + 2*cos(20))
------------------------------
                             2
1 - cos(40) + 2*(1 - cos(20)) 
$$\frac{2 l \left(-1 - \cos{\left(40 \right)} + 2 \cos{\left(20 \right)}\right)}{- \cos{\left(40 \right)} + 2 \left(- \cos{\left(20 \right)} + 1\right)^{2} + 1}$$
  /         2     \
  |      sin (20) |
l*|-1 + ----------|
  |          4    |
  \     4*sin (10)/
-------------------
           2       
        sin (20)   
   1 + ----------  
            4      
       4*sin (10)  
$$\frac{l \left(-1 + \frac{\sin^{2}{\left(20 \right)}}{4 \sin^{4}{\left(10 \right)}}\right)}{1 + \frac{\sin^{2}{\left(20 \right)}}{4 \sin^{4}{\left(10 \right)}}}$$
  /         4    \
  |    4*sin (10)|
l*|1 - ----------|
  |        2     |
  \     sin (20) /
------------------
           4      
      4*sin (10)  
  1 + ----------  
          2       
       sin (20)   
$$\frac{l \left(- \frac{4 \sin^{4}{\left(10 \right)}}{\sin^{2}{\left(20 \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(10 \right)}}{\sin^{2}{\left(20 \right)}} + 1}$$
  /           2       \
  |        csc (10)   |
l*|-1 + --------------|
  |        2/      pi\|
  |     csc |-10 + --||
  \         \      2 //
-----------------------
             2         
          csc (10)     
   1 + --------------  
          2/      pi\  
       csc |-10 + --|  
           \      2 /  
$$\frac{l \left(-1 + \frac{\csc^{2}{\left(10 \right)}}{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}\right)}{1 + \frac{\csc^{2}{\left(10 \right)}}{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}}$$
  /       2/      pi\\
  |    csc |-10 + --||
  |        \      2 /|
l*|1 - --------------|
  |          2       |
  \       csc (10)   /
----------------------
         2/      pi\  
      csc |-10 + --|  
          \      2 /  
  1 + --------------  
            2         
         csc (10)     
$$\frac{l \left(- \frac{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(10 \right)}} + 1\right)}{\frac{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(10 \right)}} + 1}$$
  /        2/     pi\\
  |     sec |10 - --||
  |         \     2 /|
l*|-1 + -------------|
  |           2      |
  \        sec (10)  /
----------------------
         2/     pi\   
      sec |10 - --|   
          \     2 /   
  1 + -------------   
            2         
         sec (10)     
$$\frac{l \left(-1 + \frac{\sec^{2}{\left(- \frac{\pi}{2} + 10 \right)}}{\sec^{2}{\left(10 \right)}}\right)}{1 + \frac{\sec^{2}{\left(- \frac{\pi}{2} + 10 \right)}}{\sec^{2}{\left(10 \right)}}}$$
  /           2      \
  |        cos (10)  |
l*|-1 + -------------|
  |        2/     pi\|
  |     cos |10 - --||
  \         \     2 //
----------------------
            2         
         cos (10)     
  1 + -------------   
         2/     pi\   
      cos |10 - --|   
          \     2 /   
$$\frac{l \left(-1 + \frac{\cos^{2}{\left(10 \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + 10 \right)}}\right)}{1 + \frac{\cos^{2}{\left(10 \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + 10 \right)}}}$$
  /       2/     pi\\
  |    cos |10 - --||
  |        \     2 /|
l*|1 - -------------|
  |          2      |
  \       cos (10)  /
---------------------
         2/     pi\  
      cos |10 - --|  
          \     2 /  
  1 + -------------  
            2        
         cos (10)    
$$\frac{l \left(- \frac{\cos^{2}{\left(- \frac{\pi}{2} + 10 \right)}}{\cos^{2}{\left(10 \right)}} + 1\right)}{\frac{\cos^{2}{\left(- \frac{\pi}{2} + 10 \right)}}{\cos^{2}{\left(10 \right)}} + 1}$$
  /          2      \
  |       sec (10)  |
l*|1 - -------------|
  |       2/     pi\|
  |    sec |10 - --||
  \        \     2 //
---------------------
            2        
         sec (10)    
  1 + -------------  
         2/     pi\  
      sec |10 - --|  
          \     2 /  
$$\frac{l \left(- \frac{\sec^{2}{\left(10 \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 10 \right)}} + 1\right)}{\frac{\sec^{2}{\left(10 \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 10 \right)}} + 1}$$
l*(1 - sec(10)^2/sec(10 - pi/2)^2)/(1 + sec(10)^2/sec(10 - pi/2)^2)