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