Дано
$$- sin^{2}{left (a + frac{15 pi}{8} right )} + cos{left (a + frac{5 pi}{8} right )}$$
Подстановка условия
$$- sin^{2}{left (a + frac{15 pi}{8} right )} + cos{left (a + frac{5 pi}{8} right )}$$
cos((5*pi)/8 + (-4)) – sin((15*pi)/8 + (-4))^2
$$- sin^{2}{left ((-4) + frac{15 pi}{8} right )} + cos{left ((-4) + frac{5 pi}{8} right )}$$
cos((5*pi)/8 – 4) – sin((15*pi)/8 – 4)^2
$$- sin^{2}{left (-4 + frac{15 pi}{8} right )} + cos{left (-4 + frac{5 pi}{8} right )}$$
-sin(4 + pi/8)^2 – cos(4 + 3*pi/8)
$$- sin^{2}{left (frac{pi}{8} + 4 right )} – cos{left (frac{3 pi}{8} + 4 right )}$$
Степени
$$- sin{left (a + frac{pi}{8} right )} – cos^{2}{left (a + frac{3 pi}{8} right )}$$
Численный ответ
-sin((15*pi)/8 + a)^2 + cos((5*pi)/8 + a)
Рациональный знаменатель
$$- sin{left (a + frac{pi}{8} right )} – cos^{2}{left (a + frac{3 pi}{8} right )}$$
Объединение рациональных выражений
$$- sin^{2}{left (frac{1}{8} left(8 a + 15 piright) right )} + cos{left (frac{1}{8} left(8 a + 5 piright) right )}$$
Общее упрощение
2/ 3*pi / pi
– cos |a + —-| – sin|a + –|
8 / 8 /
$$- sin{left (a + frac{pi}{8} right )} – cos^{2}{left (a + frac{3 pi}{8} right )}$$
Соберем выражение
$$- sin{left (a + frac{pi}{8} right )} + frac{1}{2} sin{left (2 a + frac{pi}{4} right )} – frac{1}{2}$$
Общий знаменатель
2/ 3*pi / pi
– cos |a + —-| – sin|a + –|
8 / 8 /
$$- sin{left (a + frac{pi}{8} right )} – cos^{2}{left (a + frac{3 pi}{8} right )}$$
Комбинаторика
2/ 3*pi / pi
– cos |a + —-| – sin|a + –|
8 / 8 /
$$- sin{left (a + frac{pi}{8} right )} – cos^{2}{left (a + frac{3 pi}{8} right )}$$
Раскрыть выражение
2
/ ___________ ___________ ___________ ___________
| / ___ / ___ | / ___ / ___
| / 1 / 2 / 1 / 2 | / 1 / 2 / 1 / 2
– | / – + —– *sin(a) – / – – —– *cos(a)| – / – – —– *cos(a) – / – + —– *sin(a)
/ 2 4 / 2 4 / / 2 4 / 2 4
$$- left(sqrt{frac{sqrt{2}}{4} + frac{1}{2}} sin{left (a right )} – sqrt{- frac{sqrt{2}}{4} + frac{1}{2}} cos{left (a right )}right)^{2} – sqrt{frac{sqrt{2}}{4} + frac{1}{2}} sin{left (a right )} – sqrt{- frac{sqrt{2}}{4} + frac{1}{2}} cos{left (a right )}$$
