$$\sqrt{2} \sin{\left(a \right)}$$
Рациональный знаменатель
[src]
/ pi\ / pi\
- cos|a + --| + sin|a + --|
\ 4 / \ 4 /
$$\sin{\left(a + \frac{\pi}{4} \right)} - \cos{\left(a + \frac{\pi}{4} \right)}$$
-cos(a + pi/4) + sin(a + pi/4)
/ pi\ / pi\
- cos|a + --| + sin|a + --|
\ 4 / \ 4 /
$$\sin{\left(a + \frac{\pi}{4} \right)} - \cos{\left(a + \frac{\pi}{4} \right)}$$
-cos(a + pi/4) + sin(a + pi/4)
$$\sqrt{2} \sin{\left(a \right)}$$
/ pi\ / pi\
- cos|a + --| + sin|a + --|
\ 4 / \ 4 /
$$\sin{\left(a + \frac{\pi}{4} \right)} - \cos{\left(a + \frac{\pi}{4} \right)}$$
-cos(a + pi/4) + sin(a + pi/4)
-sin(pi/4 - a) + sin(pi/4 + a)
-sin(pi/4 - a) + sin(pi/4 + a)
Объединение рациональных выражений
[src]
/pi - 4*a\ /pi + 4*a\
- sin|--------| + sin|--------|
\ 4 / \ 4 /
$$- \sin{\left(\frac{- 4 a + \pi}{4} \right)} + \sin{\left(\frac{4 a + \pi}{4} \right)}$$
-sin((pi - 4*a)/4) + sin((pi + 4*a)/4)
/ pi\ / pi\
- cos|a + --| + sin|a + --|
\ 4 / \ 4 /
$$\sin{\left(a + \frac{\pi}{4} \right)} - \cos{\left(a + \frac{\pi}{4} \right)}$$
-cos(a + pi/4) + sin(a + pi/4)
/ pi\ / pi\
- cos|a + --| + sin|a + --|
\ 4 / \ 4 /
$$\sin{\left(a + \frac{\pi}{4} \right)} - \cos{\left(a + \frac{\pi}{4} \right)}$$
/ / pi\ / pi\\ / / pi\ / pi\\
| I*|a - --| I*|-a + --|| | I*|-a - --| I*|a + --||
| \ 4 / \ 4 /| | \ 4 / \ 4 /|
I*\- e + e / I*\- e + e /
-------------------------------- - --------------------------------
2 2
$$- \frac{i \left(- e^{i \left(- a - \frac{\pi}{4}\right)} + e^{i \left(a + \frac{\pi}{4}\right)}\right)}{2} + \frac{i \left(e^{i \left(- a + \frac{\pi}{4}\right)} - e^{i \left(a - \frac{\pi}{4}\right)}\right)}{2}$$
i*(-exp(i*(a - pi/4)) + exp(i*(-a + pi/4)))/2 - i*(-exp(i*(-a - pi/4)) + exp(i*(a + pi/4)))/2