General simplification
[src]
2 / 3*x\
2*sin (y) + cos|-y + ---|*sin(-y + 2*x)
\ 2 /
$$2 \sin^{2}{\left(y \right)} + \sin{\left(2 x - y \right)} \cos{\left(\frac{3 x}{2} - y \right)}$$
2*sin(y)^2 + cos(-y + 3*x/2)*sin(-y + 2*x)
/ 3*x\
cos|-y + ---|*sin(-y + 2*x) + 2*cos(y)*sin(y)*tan(y)
\ 2 /
$$2 \sin{\left(y \right)} \cos{\left(y \right)} \tan{\left(y \right)} + \sin{\left(2 x - y \right)} \cos{\left(\frac{3 x}{2} - y \right)}$$
cos(-y + 3*x/2)*sin(-y + 2*x) + 2*cos(y)*sin(y)*tan(y)
/ 3*x\
cos|-y + ---|*sin(-y + 2*x) + 2*cos(y)*sin(y)*tan(y)
\ 2 /
$$2 \sin{\left(y \right)} \cos{\left(y \right)} \tan{\left(y \right)} + \sin{\left(2 x - y \right)} \cos{\left(\frac{3 x}{2} - y \right)}$$
/ / 3*x\ / 3*x\\
| I*|y - ---| I*|-y + ---||
| \ 2 / \ 2 /| / / pi\ / pi\\
|e e | / I*(y - 2*x) I*(-y + 2*x)\ | I*|y + --| I*|-y - --|| / / 3*pi\ / 3*pi\\
I*|------------ + -------------|*\- e + e / | \ 2 / \ 2 /| | I*|-y + ----| I*|y - ----||
\ 2 2 / |e e | | \ 2 / \ 2 /|
- ----------------------------------------------------------------- + I*|----------- + ------------|*\- e + e /*tan(y)
2 \ 2 2 /
$$- \frac{i \left(- e^{i \left(- 2 x + y\right)} + e^{i \left(2 x - y\right)}\right) \left(\frac{e^{i \left(- \frac{3 x}{2} + y\right)}}{2} + \frac{e^{i \left(\frac{3 x}{2} - y\right)}}{2}\right)}{2} + i \left(\frac{e^{i \left(- y - \frac{\pi}{2}\right)}}{2} + \frac{e^{i \left(y + \frac{\pi}{2}\right)}}{2}\right) \left(- e^{i \left(- y + \frac{3 \pi}{2}\right)} + e^{i \left(y - \frac{3 \pi}{2}\right)}\right) \tan{\left(y \right)}$$
-i*(exp(i*(y - 3*x/2))/2 + exp(i*(-y + 3*x/2))/2)*(-exp(i*(y - 2*x)) + exp(i*(-y + 2*x)))/2 + i*(exp(i*(y + pi/2))/2 + exp(i*(-y - pi/2))/2)*(-exp(i*(-y + 3*pi/2)) + exp(i*(y - 3*pi/2)))*tan(y)
/ 3*x\
cos|-y + ---|*sin(-y + 2*x) + 2*cos(y)*sin(y)*tan(y)
\ 2 /
$$2 \sin{\left(y \right)} \cos{\left(y \right)} \tan{\left(y \right)} + \sin{\left(2 x - y \right)} \cos{\left(\frac{3 x}{2} - y \right)}$$
cos(-y + 3*x/2)*sin(-y + 2*x) + 2*cos(y)*sin(y)*tan(y)
cos(y - 3*x/2)*sin(2*x - y) - 2.0*cos(pi/2 + y)*cot(pi/2 - y)*sin(y - 3*pi/2)
cos(y - 3*x/2)*sin(2*x - y) - 2.0*cos(pi/2 + y)*cot(pi/2 - y)*sin(y - 3*pi/2)
Rational denominator
[src]
/ 3*x\ / pi\ / pi\
cos|-y + ---|*sin(-y + 2*x) + 2*cos(y)*cos|y + --|*cot|y - --|
\ 2 / \ 2 / \ 2 /
$$\sin{\left(2 x - y \right)} \cos{\left(\frac{3 x}{2} - y \right)} + 2 \cos{\left(y \right)} \cos{\left(y + \frac{\pi}{2} \right)} \cot{\left(y - \frac{\pi}{2} \right)}$$
cos(-y + 3*x/2)*sin(-y + 2*x) + 2*cos(y)*cos(y + pi/2)*cot(y - pi/2)
Combining rational expressions
[src]
/-3*x + 2*y\ /pi + 2*y\ /pi - 2*y\ /-3*pi + 2*y\
cos|----------|*sin(-y + 2*x) - 2*cos|--------|*cot|--------|*sin|-----------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\sin{\left(2 x - y \right)} \cos{\left(\frac{- 3 x + 2 y}{2} \right)} - 2 \sin{\left(\frac{2 y - 3 \pi}{2} \right)} \cos{\left(\frac{2 y + \pi}{2} \right)} \cot{\left(\frac{\pi - 2 y}{2} \right)}$$
cos((-3*x + 2*y)/2)*sin(-y + 2*x) - 2*cos((pi + 2*y)/2)*cot((pi - 2*y)/2)*sin((-3*pi + 2*y)/2)
Assemble expression
[src]
/ 3*x\ /pi \ /pi \ / 3*pi\
cos|y - ---|*sin(2*x - y) - 2*cos|-- + y|*cot|-- - y|*sin|y - ----|
\ 2 / \2 / \2 / \ 2 /
$$\sin{\left(2 x - y \right)} \cos{\left(- \frac{3 x}{2} + y \right)} - 2 \sin{\left(y - \frac{3 \pi}{2} \right)} \cos{\left(y + \frac{\pi}{2} \right)} \cot{\left(- y + \frac{\pi}{2} \right)}$$
cos(y - 3*x/2)*sin(2*x - y) - 2*cos(pi/2 + y)*cot(pi/2 - y)*sin(y - 3*pi/2)
2 /3*x\ /3*x\ 2 2 /3*x\ 2 /3*x\ 2 /3*x\ /3*x\
sin (y)*sin|---| + cos(y)*cos|---|*sin(y) - 2*cos (x)*sin (y)*sin|---| + 2*cos(y)*sin(y)*tan(y) - 2*cos (x)*cos(y)*cos|---|*sin(y) + 2*cos (y)*cos(x)*cos|---|*sin(x) + 2*cos(x)*cos(y)*sin(x)*sin(y)*sin|---|
\ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
$$2 \sin{\left(x \right)} \sin{\left(\frac{3 x}{2} \right)} \sin{\left(y \right)} \cos{\left(x \right)} \cos{\left(y \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)} \cos{\left(\frac{3 x}{2} \right)} \cos^{2}{\left(y \right)} - 2 \sin{\left(\frac{3 x}{2} \right)} \sin^{2}{\left(y \right)} \cos^{2}{\left(x \right)} + \sin{\left(\frac{3 x}{2} \right)} \sin^{2}{\left(y \right)} - 2 \sin{\left(y \right)} \cos^{2}{\left(x \right)} \cos{\left(\frac{3 x}{2} \right)} \cos{\left(y \right)} + \sin{\left(y \right)} \cos{\left(\frac{3 x}{2} \right)} \cos{\left(y \right)} + 2 \sin{\left(y \right)} \cos{\left(y \right)} \tan{\left(y \right)}$$
sin(y)^2*sin(3*x/2) + cos(y)*cos(3*x/2)*sin(y) - 2*cos(x)^2*sin(y)^2*sin(3*x/2) + 2*cos(y)*sin(y)*tan(y) - 2*cos(x)^2*cos(y)*cos(3*x/2)*sin(y) + 2*cos(y)^2*cos(x)*cos(3*x/2)*sin(x) + 2*cos(x)*cos(y)*sin(x)*sin(y)*sin(3*x/2)