Дано
$$sin^{2}{left (- a + p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (- a + 2 p right )}$$
Подстановка условия
$$sin^{2}{left (- a + p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (- a + 2 p right )}$$
sin(p – (4))^2 + sin((3*p)/2 + (4)) – cos(2*p – (4))
$$sin^{2}{left (- (4) + p right )} + sin{left ((4) + frac{3 p}{2} right )} – cos{left (- (4) + 2 p right )}$$
sin(p – 4)^2 + sin((3*p)/2 + 4) – cos(2*p – 4)
$$sin^{2}{left (p – 4 right )} + sin{left (frac{3 p}{2} + 4 right )} – cos{left (2 p – 4 right )}$$
sin(-4 + p)^2 – cos(-4 + 2*p) + sin(4 + 3*p/2)
$$sin^{2}{left (p – 4 right )} + sin{left (frac{3 p}{2} + 4 right )} – cos{left (2 p – 4 right )}$$
Степени
$$sin^{2}{left (a – p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )}$$
Численный ответ
sin(p – a)^2 – cos(2*p – a) + sin((3*p)/2 + a)
Рациональный знаменатель
$$sin^{2}{left (a – p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )}$$
Объединение рациональных выражений
$$sin^{2}{left (a – p right )} + sin{left (frac{1}{2} left(2 a + 3 pright) right )} – cos{left (a – 2 p right )}$$
Общее упрощение
2 / 3*p
sin (a – p) – cos(a – 2*p) + sin|a + —|
2 /
$$sin^{2}{left (a – p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )}$$
Соберем выражение
$$sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )} – frac{1}{2} cos{left (2 a – 2 p right )} + frac{1}{2}$$
Общий знаменатель
2 / 3*p
sin (p – a) – cos(a – 2*p) + sin|a + —|
2 /
$$sin^{2}{left (- a + p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )}$$
Тригонометрическая часть
2 / 3*p
sin (p – a) – cos(a – 2*p) + sin|a + —|
2 /
$$sin^{2}{left (- a + p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )}$$
Комбинаторика
2 / 3*p
sin (a – p) – cos(a – 2*p) + sin|a + —|
2 /
$$sin^{2}{left (a – p right )} + sin{left (a + frac{3 p}{2} right )} – cos{left (a – 2 p right )}$$
Раскрыть выражение
2 /3*p /3*p
(cos(a)*sin(p) – cos(p)*sin(a)) + cos(a)*sin|—| + cos|—|*sin(a) – cos(a)*cos(2*p) – sin(a)*sin(2*p)
2 / 2 /
$$left(- sin{left (a right )} cos{left (p right )} + sin{left (p right )} cos{left (a right )}right)^{2} – sin{left (a right )} sin{left (2 p right )} + sin{left (a right )} cos{left (frac{3 p}{2} right )} + sin{left (frac{3 p}{2} right )} cos{left (a right )} – cos{left (a right )} cos{left (2 p right )}$$
