2 2/ pi\ / pi\
1 - sin (a)*sin |a + --|*cot|a + --|
\ 4 / \ 4 /
$$- \sin^{2}{\left (a \right )} \sin^{2}{\left (a + \frac{\pi}{4} \right )} \cot{\left (a + \frac{\pi}{4} \right )} + 1$$
1.0 - 1.0*cos(pi/4 - a)^2*sin(a)^2*cot(pi/4 + a)
Рациональный знаменатель
[src] 2 2/pi + 4*a\ / pi\
1 - sin (a)*sin |--------|*cot|a + --|
\ 4 / \ 4 /
$$- \sin^{2}{\left (a \right )} \sin^{2}{\left (\frac{1}{4} \left(4 a + \pi\right) \right )} \cot{\left (a + \frac{\pi}{4} \right )} + 1$$
Объединение рациональных выражений
[src] 2/pi - 4*a\ 2 /pi + 4*a\
1 - cos |--------|*sin (a)*cot|--------|
\ 4 / \ 4 /
$$- \sin^{2}{\left (a \right )} \cos^{2}{\left (\frac{1}{4} \left(- 4 a + \pi\right) \right )} \cot{\left (\frac{1}{4} \left(4 a + \pi\right) \right )} + 1$$
2
4 sin (a)
1 + sin (a) - -------
2
$$\sin^{4}{\left (a \right )} - \frac{1}{2} \sin^{2}{\left (a \right )} + 1$$
/1 cos(2*a) sin(4*a) sin(2*a)\ / pi\
1 - |- - -------- - -------- + --------|*cot|a + --|
\4 4 8 4 / \ 4 /
$$- \left(\frac{1}{4} \sin{\left (2 a \right )} - \frac{1}{8} \sin{\left (4 a \right )} - \frac{1}{4} \cos{\left (2 a \right )} + \frac{1}{4}\right) \cot{\left (a + \frac{\pi}{4} \right )} + 1$$
2 2/ pi\ / pi\
1 - sin (a)*sin |a + --|*cot|a + --|
\ 4 / \ 4 /
$$- \sin^{2}{\left (a \right )} \sin^{2}{\left (a + \frac{\pi}{4} \right )} \cot{\left (a + \frac{\pi}{4} \right )} + 1$$
2 2/ pi\ / pi\
1 - sin (a)*sin |a + --|*cot|a + --|
\ 4 / \ 4 /
$$- \sin^{2}{\left (a \right )} \sin^{2}{\left (a + \frac{\pi}{4} \right )} \cot{\left (a + \frac{\pi}{4} \right )} + 1$$
Тригонометрическая часть
[src] 2
4 sin (a)
1 + sin (a) - -------
2
$$\sin^{4}{\left (a \right )} - \frac{1}{2} \sin^{2}{\left (a \right )} + 1$$
2
/ ___ ___ \
|\/ 2 *cos(a) \/ 2 *sin(a)| 2
|------------ + ------------| *sin (a)*(-1 + cot(a))
\ 2 2 /
1 - ----------------------------------------------------
1 + cot(a)
$$- \frac{\left(\frac{\sqrt{2}}{2} \sin{\left (a \right )} + \frac{\sqrt{2}}{2} \cos{\left (a \right )}\right)^{2}}{\cot{\left (a \right )} + 1} \left(\cot{\left (a \right )} - 1\right) \sin^{2}{\left (a \right )} + 1$$