Господин Экзамен
cos(2)*x если x=4
Решение
Подстановка условия
[src]
cos(2)*x при x = 4
подставляем
cos(2)*x
$$x \cos{\left(2 \right)}$$
x*cos(2)
$$x \cos{\left(2 \right)}$$
переменные
x = 4
$$x = 4$$
(4)*cos(2)
$$(4) \cos{\left(2 \right)}$$
4*cos(2)
$$4 \cos{\left(2 \right)}$$
4*cos(2)
Степени
[src]
/ -2*I 2*I\ |e e | x*|----- + ----| \ 2 2 /
$$x \left(\frac{e^{- 2 i}}{2} + \frac{e^{2 i}}{2}\right)$$
x*(exp(-2*i)/2 + exp(2*i)/2)
Тригонометрическая часть
[src]
x ------ sec(2)
$$\frac{x}{\sec{\left(2 \right)}}$$
/ pi\
x*sin|2 + --|
\ 2 /
$$x \sin{\left(\frac{\pi}{2} + 2 \right)}$$
x ------------ / pi\ csc|-2 + --| \ 2 /
$$\frac{x}{\csc{\left(-2 + \frac{\pi}{2} \right)}}$$
/ pi\
x*(1 + sin(2))*cot|1 + --|
\ 4 /
$$x \left(\sin{\left(2 \right)} + 1\right) \cot{\left(\frac{\pi}{4} + 1 \right)}$$
/ 2 \
x*\-1 + cot (1)/
----------------
2
1 + cot (1)
$$\frac{x \left(-1 + \cot^{2}{\left(1 \right)}\right)}{\cot^{2}{\left(1 \right)} + 1}$$
/ 2 \
x*\1 - tan (1)/
---------------
2
1 + tan (1)
$$\frac{x \left(- \tan^{2}{\left(1 \right)} + 1\right)}{1 + \tan^{2}{\left(1 \right)}}$$
/ pi\
2*x*cot|1 + --|
\ 4 /
----------------
2/ pi\
1 + cot |1 + --|
\ 4 /
$$\frac{2 x \cot{\left(\frac{\pi}{4} + 1 \right)}}{\cot^{2}{\left(\frac{\pi}{4} + 1 \right)} + 1}$$
/ pi\
2*x*tan|1 + --|
\ 4 /
----------------
2/ pi\
1 + tan |1 + --|
\ 4 /
$$\frac{2 x \tan{\left(\frac{\pi}{4} + 1 \right)}}{1 + \tan^{2}{\left(\frac{\pi}{4} + 1 \right)}}$$
/ 1 \
x*|-1 + -------|
| 2 |
\ tan (1)/
----------------
1
1 + -------
2
tan (1)
$$\frac{x \left(-1 + \frac{1}{\tan^{2}{\left(1 \right)}}\right)}{\frac{1}{\tan^{2}{\left(1 \right)}} + 1}$$
/ 1 \
x*|1 - -------|
| 2 |
\ cot (1)/
---------------
1
1 + -------
2
cot (1)
$$\frac{x \left(- \frac{1}{\cot^{2}{\left(1 \right)}} + 1\right)}{1 + \frac{1}{\cot^{2}{\left(1 \right)}}}$$
2*x*(-1 - cos(4) + 2*cos(2))
----------------------------
2
1 - cos(4) + 2*(1 - cos(2))
$$\frac{2 x \left(-1 + 2 \cos{\left(2 \right)} - \cos{\left(4 \right)}\right)}{- \cos{\left(4 \right)} + 1 + 2 \left(- \cos{\left(2 \right)} + 1\right)^{2}}$$
/ 2 \
| sin (2) |
4*x*|-1 + ---------|
| 4 |
\ 4*sin (1)/
--------------------
2
sin (2)
4 + -------
4
sin (1)
$$\frac{4 x \left(-1 + \frac{\sin^{2}{\left(2 \right)}}{4 \sin^{4}{\left(1 \right)}}\right)}{\frac{\sin^{2}{\left(2 \right)}}{\sin^{4}{\left(1 \right)}} + 4}$$
/ 2 \
| sin (2) |
x*|-1 + ---------|
| 4 |
\ 4*sin (1)/
------------------
2
sin (2)
1 + ---------
4
4*sin (1)
$$\frac{x \left(-1 + \frac{\sin^{2}{\left(2 \right)}}{4 \sin^{4}{\left(1 \right)}}\right)}{\frac{\sin^{2}{\left(2 \right)}}{4 \sin^{4}{\left(1 \right)}} + 1}$$
/ 4 \
| 4*sin (1)|
x*|1 - ---------|
| 2 |
\ sin (2) /
-----------------
4
4*sin (1)
1 + ---------
2
sin (2)
$$\frac{x \left(- \frac{4 \sin^{4}{\left(1 \right)}}{\sin^{2}{\left(2 \right)}} + 1\right)}{1 + \frac{4 \sin^{4}{\left(1 \right)}}{\sin^{2}{\left(2 \right)}}}$$
/ 2 \
| csc (1) |
x*|-1 + -------------|
| 2/ pi\|
| csc |-1 + --||
\ \ 2 //
----------------------
2
csc (1)
1 + -------------
2/ pi\
csc |-1 + --|
\ 2 /
$$\frac{x \left(-1 + \frac{\csc^{2}{\left(1 \right)}}{\csc^{2}{\left(-1 + \frac{\pi}{2} \right)}}\right)}{\frac{\csc^{2}{\left(1 \right)}}{\csc^{2}{\left(-1 + \frac{\pi}{2} \right)}} + 1}$$
/ 2/ pi\\
| csc |-1 + --||
| \ 2 /|
x*|1 - -------------|
| 2 |
\ csc (1) /
---------------------
2/ pi\
csc |-1 + --|
\ 2 /
1 + -------------
2
csc (1)
$$\frac{x \left(- \frac{\csc^{2}{\left(-1 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(1 \right)}} + 1\right)}{1 + \frac{\csc^{2}{\left(-1 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(1 \right)}}}$$
/ 2 \
| cos (1) |
x*|-1 + ------------|
| 2/ pi\|
| cos |1 - --||
\ \ 2 //
---------------------
2
cos (1)
1 + ------------
2/ pi\
cos |1 - --|
\ 2 /
$$\frac{x \left(-1 + \frac{\cos^{2}{\left(1 \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + 1 \right)}}\right)}{\frac{\cos^{2}{\left(1 \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + 1 \right)}} + 1}$$
/ 2/ pi\\
| sec |1 - --||
| \ 2 /|
x*|-1 + ------------|
| 2 |
\ sec (1) /
---------------------
2/ pi\
sec |1 - --|
\ 2 /
1 + ------------
2
sec (1)
$$\frac{x \left(-1 + \frac{\sec^{2}{\left(- \frac{\pi}{2} + 1 \right)}}{\sec^{2}{\left(1 \right)}}\right)}{\frac{\sec^{2}{\left(- \frac{\pi}{2} + 1 \right)}}{\sec^{2}{\left(1 \right)}} + 1}$$
/ 2 \
| sec (1) |
x*|1 - ------------|
| 2/ pi\|
| sec |1 - --||
\ \ 2 //
--------------------
2
sec (1)
1 + ------------
2/ pi\
sec |1 - --|
\ 2 /
$$\frac{x \left(- \frac{\sec^{2}{\left(1 \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 1 \right)}} + 1\right)}{1 + \frac{\sec^{2}{\left(1 \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 1 \right)}}}$$
/ 2/ pi\\
| cos |1 - --||
| \ 2 /|
x*|1 - ------------|
| 2 |
\ cos (1) /
--------------------
2/ pi\
cos |1 - --|
\ 2 /
1 + ------------
2
cos (1)
$$\frac{x \left(- \frac{\cos^{2}{\left(- \frac{\pi}{2} + 1 \right)}}{\cos^{2}{\left(1 \right)}} + 1\right)}{1 + \frac{\cos^{2}{\left(- \frac{\pi}{2} + 1 \right)}}{\cos^{2}{\left(1 \right)}}}$$
x*(1 - cos(1 - pi/2)^2/cos(1)^2)/(1 + cos(1 - pi/2)^2/cos(1)^2)