Господин Экзамен
Общий знаменатель (sin(690*pi)/360+cos(3180*pi)/360+tan(675))/(-10)
Решение
Вы ввели
[src]
sin(690*pi) cos(3180*pi)
----------- + ------------ + tan(675)
360 360
-------------------------------------
-10
$$\frac{\tan{\left(675 \right)} + \frac{\sin{\left(690 \pi \right)}}{360} + \frac{\cos{\left(3180 \pi \right)}}{360}}{-10}$$
(sin(690*pi)/360 + cos(3180*pi)/360 + tan(675))/(-10)
Общее упрощение
[src]
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
-1/3600 - tan(675)/10
Собрать выражение
[src]
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
-1/3600 - tan(675)/10
Общий знаменатель
[src]
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
-1/3600 - tan(675)/10
Степени
[src]
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
/ 675*I -675*I\
1 I*\- e + e /
- ---- - ----------------------
3600 / -675*I 675*I\
10*\e + e /
$$- \frac{1}{3600} - \frac{i \left(e^{- 675 i} - e^{675 i}\right)}{10 \left(e^{- 675 i} + e^{675 i}\right)}$$
tan(675) cos(3180*pi) sin(690*pi)
- -------- - ------------ - -----------
10 3600 3600
$$- \frac{\cos{\left(3180 \pi \right)}}{3600} - \frac{\sin{\left(690 \pi \right)}}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
-tan(675)/10 - cos(3180*pi)/3600 - sin(690*pi)/3600
Комбинаторика
[src]
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
-1/3600 - tan(675)/10
Рациональный знаменатель
[src]
-1 - 360*tan(675)
-----------------
3600
$$\frac{-1 - 360 \tan{\left(675 \right)}}{3600}$$
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
-1/3600 - tan(675)/10
Тригонометрическая часть
[src]
1 tan(675) - ---- - -------- 3600 10
$$- \frac{1}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
1 1 - ---- - ----------- 3600 10*cot(675)
$$- \frac{1}{3600} - \frac{1}{10 \cot{\left(675 \right)}}$$
1 sin(675) - ---- - ----------- 3600 10*cos(675)
$$- \frac{1}{3600} - \frac{\sin{\left(675 \right)}}{10 \cos{\left(675 \right)}}$$
1 sec(675) - ---- - ----------- 3600 10*csc(675)
$$- \frac{1}{3600} - \frac{\sec{\left(675 \right)}}{10 \csc{\left(675 \right)}}$$
1 csc(1350)
- ---- - -----------
3600 2
5*csc (675)
$$- \frac{1}{3600} - \frac{\csc{\left(1350 \right)}}{5 \csc^{2}{\left(675 \right)}}$$
2 1 sin (675)*csc(1350) - ---- - ------------------- 3600 5
$$- \frac{1}{3600} - \frac{\sin^{2}{\left(675 \right)} \csc{\left(1350 \right)}}{5}$$
2 1 sin (675) - ---- - ----------- 3600 5*sin(1350)
$$- \frac{1}{3600} - \frac{\sin^{2}{\left(675 \right)}}{5 \sin{\left(1350 \right)}}$$
1 sin(675)
- ---- - ----------------
3600 / pi\
10*sin|675 + --|
\ 2 /
$$- \frac{1}{3600} - \frac{\sin{\left(675 \right)}}{10 \sin{\left(\frac{\pi}{2} + 675 \right)}}$$
/ pi\
csc|-675 + --|
1 \ 2 /
- ---- - --------------
3600 10*csc(675)
$$- \frac{1}{3600} - \frac{\csc{\left(-675 + \frac{\pi}{2} \right)}}{10 \csc{\left(675 \right)}}$$
1 sec(675)
- ---- - -----------------
3600 / pi\
10*sec|-675 + --|
\ 2 /
$$- \frac{1}{3600} - \frac{\sec{\left(675 \right)}}{10 \sec{\left(-675 + \frac{\pi}{2} \right)}}$$
/ pi\
cos|675 - --|
1 \ 2 /
- ---- - -------------
3600 10*cos(675)
$$- \frac{1}{3600} - \frac{\cos{\left(- \frac{\pi}{2} + 675 \right)}}{10 \cos{\left(675 \right)}}$$
1 sec(675)
- ---- - ----------------
3600 / pi\
10*sec|675 - --|
\ 2 /
$$- \frac{1}{3600} - \frac{\sec{\left(675 \right)}}{10 \sec{\left(- \frac{\pi}{2} + 675 \right)}}$$
2/ pi\
cos |675 - --|
1 \ 2 /
- ---- - ----------------
3600 / pi\
5*cos|1350 - --|
\ 2 /
$$- \frac{1}{3600} - \frac{\cos^{2}{\left(- \frac{\pi}{2} + 675 \right)}}{5 \cos{\left(- \frac{\pi}{2} + 1350 \right)}}$$
/ pi\
sec|1350 - --|
1 \ 2 /
- ---- - ----------------
3600 2/ pi\
5*sec |675 - --|
\ 2 /
$$- \frac{1}{3600} - \frac{\sec{\left(- \frac{\pi}{2} + 1350 \right)}}{5 \sec^{2}{\left(- \frac{\pi}{2} + 675 \right)}}$$
/6361*pi\
sin|-------| 2
\ 2 / sin (675)
- ------------ - -----------
3600 5*sin(1350)
$$- \frac{\sin{\left(\frac{6361 \pi}{2} \right)}}{3600} - \frac{\sin^{2}{\left(675 \right)}}{5 \sin{\left(1350 \right)}}$$
tan(675) cos(3180*pi) sin(690*pi)
- -------- - ------------ - -----------
10 3600 3600
$$- \frac{\cos{\left(3180 \pi \right)}}{3600} - \frac{\sin{\left(690 \pi \right)}}{3600} - \frac{\tan{\left(675 \right)}}{10}$$
1 tan(675/2)
- ---- - -------------------
3600 / 2 \
5*\1 - tan (675/2)/
$$- \frac{1}{3600} - \frac{\tan{\left(\frac{675}{2} \right)}}{5 \cdot \left(- \tan^{2}{\left(\frac{675}{2} \right)} + 1\right)}$$
1 sin(690*pi) sin(675)
- ---- - ----------- - ----------------
3600 3600 / pi\
10*sin|675 + --|
\ 2 /
$$- \frac{1}{3600} - \frac{\sin{\left(690 \pi \right)}}{3600} - \frac{\sin{\left(675 \right)}}{10 \sin{\left(\frac{\pi}{2} + 675 \right)}}$$
2/ pi\
cos |675 - --|
cos(3180*pi) \ 2 /
- ------------ - ----------------
3600 / pi\
5*cos|1350 - --|
\ 2 /
$$- \frac{\cos{\left(3180 \pi \right)}}{3600} - \frac{\cos^{2}{\left(- \frac{\pi}{2} + 675 \right)}}{5 \cos{\left(- \frac{\pi}{2} + 1350 \right)}}$$
/ pi\
sec|1350 - --|
1 \ 2 /
- ----------------- - ----------------
3600*sec(3180*pi) 2/ pi\
5*sec |675 - --|
\ 2 /
$$- \frac{1}{3600 \sec{\left(3180 \pi \right)}} - \frac{\sec{\left(- \frac{\pi}{2} + 1350 \right)}}{5 \sec^{2}{\left(- \frac{\pi}{2} + 675 \right)}}$$
/ pi\
csc|-675 + --|
1 1 \ 2 /
- ---- - ----------------- - -----------------
3600 3600*csc(-689*pi) 10*csc(-675 + pi)
$$- \frac{1}{3600} - \frac{1}{3600 \csc{\left(- 689 \pi \right)}} - \frac{\csc{\left(-675 + \frac{\pi}{2} \right)}}{10 \csc{\left(-675 + \pi \right)}}$$
/1379*pi\ / pi\
cos|-------| cos|675 - --|
1 \ 2 / \ 2 /
- ---- - ------------ - -------------
3600 3600 10*cos(675)
$$- \frac{1}{3600} - \frac{\cos{\left(\frac{1379 \pi}{2} \right)}}{3600} - \frac{\cos{\left(- \frac{\pi}{2} + 675 \right)}}{10 \cos{\left(675 \right)}}$$
1 1 sec(675)
- ---- - ----------------- - ----------------
3600 /1379*pi\ / pi\
3600*sec|-------| 10*sec|675 - --|
\ 2 / \ 2 /
$$- \frac{1}{3600} - \frac{1}{3600 \sec{\left(\frac{1379 \pi}{2} \right)}} - \frac{\sec{\left(675 \right)}}{10 \sec{\left(- \frac{\pi}{2} + 675 \right)}}$$
2
1 4*tan (675/2)
- ---- - ------------------------------
3600 2
/ 2 \
5*\1 + tan (675/2)/ *sin(1350)
$$- \frac{1}{3600} - \frac{4 \tan^{2}{\left(\frac{675}{2} \right)}}{5 \left(1 + \tan^{2}{\left(\frac{675}{2} \right)}\right)^{2} \sin{\left(1350 \right)}}$$
/ 1 1 \
|--------------- + ----------------|*sin(675)
| 1 2 |
|1 - ----------- -1 + tan (675/2)|
| 2 |
1 \ tan (675/2) /
- ---- + ---------------------------------------------
3600 10
$$- \frac{1}{3600} + \frac{\left(\frac{1}{-1 + \tan^{2}{\left(\frac{675}{2} \right)}} + \frac{1}{- \frac{1}{\tan^{2}{\left(\frac{675}{2} \right)}} + 1}\right) \sin{\left(675 \right)}}{10}$$
2 / 2 \
1 2*tan (675/2)*\1 + tan (675)/
- ---- - -----------------------------
3600 2
/ 2 \
5*\1 + tan (675/2)/ *tan(675)
$$- \frac{1}{3600} - \frac{2 \left(\tan^{2}{\left(675 \right)} + 1\right) \tan^{2}{\left(\frac{675}{2} \right)}}{5 \left(1 + \tan^{2}{\left(\frac{675}{2} \right)}\right)^{2} \tan{\left(675 \right)}}$$
2 / 2 \
1 2*cot (675/2)*\1 + cot (675)/
- ---- - -----------------------------
3600 2
/ 2 \
5*\1 + cot (675/2)/ *cot(675)
$$- \frac{1}{3600} - \frac{2 \cdot \left(1 + \cot^{2}{\left(675 \right)}\right) \cot^{2}{\left(\frac{675}{2} \right)}}{5 \left(\cot^{2}{\left(\frac{675}{2} \right)} + 1\right)^{2} \cot{\left(675 \right)}}$$
/ 2/675 pi\\
|1 + tan |--- + --||*cot(675/2)
1 \ \ 2 4 //
- ---- - ----------------------------------
3600 / 2 \ /675 pi\
10*\1 + cot (675/2)/*tan|--- + --|
\ 2 4 /
$$- \frac{1}{3600} - \frac{\left(1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{675}{2} \right)}\right) \cot{\left(\frac{675}{2} \right)}}{10 \left(\cot^{2}{\left(\frac{675}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{4} + \frac{675}{2} \right)}}$$
/ 2 \ / 2/675 pi\\
\1 + tan (675/2)/*|1 - cot |--- + --||*(1 + sin(675))
1 \ \ 2 4 //
- ---- - -----------------------------------------------------
3600 / 2 \
20*\1 - tan (675/2)/
$$- \frac{1}{3600} - \frac{\left(1 + \tan^{2}{\left(\frac{675}{2} \right)}\right) \left(- \cot^{2}{\left(\frac{\pi}{4} + \frac{675}{2} \right)} + 1\right) \left(\sin{\left(675 \right)} + 1\right)}{20 \cdot \left(- \tan^{2}{\left(\frac{675}{2} \right)} + 1\right)}$$
/ 2 \ / 2/675 pi\\
\1 + cot (675/2)/*|-1 + tan |--- + --||
1 \ \ 2 4 //
- ---- - ------------------------------------------
3600 / 2/675 pi\\ / 2 \
10*|1 + tan |--- + --||*\-1 + cot (675/2)/
\ \ 2 4 //
$$- \frac{1}{3600} - \frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{675}{2} \right)}\right) \left(\cot^{2}{\left(\frac{675}{2} \right)} + 1\right)}{10 \left(-1 + \cot^{2}{\left(\frac{675}{2} \right)}\right) \left(1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{675}{2} \right)}\right)}$$
/ 2 \ / 2/675 pi\\
\1 + tan (675/2)/*|1 - cot |--- + --||
1 \ \ 2 4 //
- ---- - -----------------------------------------
3600 / 2/675 pi\\ / 2 \
10*|1 + cot |--- + --||*\1 - tan (675/2)/
\ \ 2 4 //
$$- \frac{1}{3600} - \frac{\left(1 + \tan^{2}{\left(\frac{675}{2} \right)}\right) \left(- \cot^{2}{\left(\frac{\pi}{4} + \frac{675}{2} \right)} + 1\right)}{10 \cdot \left(- \tan^{2}{\left(\frac{675}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{4} + \frac{675}{2} \right)} + 1\right)}$$
-1/3600 - (1 + tan(675/2)^2)*(1 - cot(675/2 + pi/4)^2)/(10*(1 + cot(675/2 + pi/4)^2)*(1 - tan(675/2)^2))
Объединение рациональных выражений
[src]
-(1 + 360*tan(675))
--------------------
3600
$$- \frac{360 \tan{\left(675 \right)} + 1}{3600}$$
-(1 + 360*tan(675))/3600