Дано

$$frac{1}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right) cos{left (a right )}$$
Подстановка условия
$$frac{1}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right) cos{left (a right )}$$

((sin((1/4))^4 – cos((1/4))^4)/sin((1/4)))*cos((1/4))

$$frac{1}{sin{left ((1/4) right )}} left(sin^{4}{left ((1/4) right )} – cos^{4}{left ((1/4) right )}right) cos{left ((1/4) right )}$$

((sin(1/4)^4 – cos(1/4)^4)/sin(1/4))*cos(1/4)

$$frac{1}{sin{left (frac{1}{4} right )}} left(- cos^{4}{left (frac{1}{4} right )} + sin^{4}{left (frac{1}{4} right )}right) cos{left (frac{1}{4} right )}$$

(sin(1/4)^4 – cos(1/4)^4)*cos(1/4)/sin(1/4)

$$frac{cos{left (frac{1}{4} right )}}{sin{left (frac{1}{4} right )}} left(- cos^{4}{left (frac{1}{4} right )} + sin^{4}{left (frac{1}{4} right )}right)$$
Степени
$$frac{cos{left (a right )}}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right)$$
Численный ответ

(sin(a)^4 – cos(a)^4)*cos(a)/sin(a)

Рациональный знаменатель
$$frac{cos{left (a right )}}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right)$$
Объединение рациональных выражений
$$frac{cos{left (a right )}}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right)$$
Общее упрощение

-cos(2*a)
———-
tan(a)

$$- frac{cos{left (2 a right )}}{tan{left (a right )}}$$
Соберем выражение
$$- cos{left (2 a right )} cot{left (a right )}$$

/ 4 4
sin (a) – cos (a)/*cos(a)
————————–
sin(a)

$$frac{cos{left (a right )}}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right)$$
Общий знаменатель

5
3 cos (a)
sin (a)*cos(a) – ——-
sin(a)

$$sin^{3}{left (a right )} cos{left (a right )} – frac{cos^{5}{left (a right )}}{sin{left (a right )}}$$
Тригонометрическая часть

-cos(2*a)
———-
tan(a)

$$- frac{cos{left (2 a right )}}{tan{left (a right )}}$$
Комбинаторика

/ 2 2
-cos (a) + sin (a)/*(-sin(a) + cos(a))*(cos(a) + sin(a))*cos(a)
—————————————————————–
sin(a)

$$- frac{cos{left (a right )}}{sin{left (a right )}} left(- sin{left (a right )} + cos{left (a right )}right) left(sin{left (a right )} + cos{left (a right )}right) left(sin^{2}{left (a right )} + cos^{2}{left (a right )}right)$$
Раскрыть выражение

/ 4 4
sin (a) – cos (a)/*cos(a)
————————–
sin(a)

$$frac{cos{left (a right )}}{sin{left (a right )}} left(sin^{4}{left (a right )} – cos^{4}{left (a right )}right)$$
   
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Yanahelp
НТУ "ХПИ", 2012 г., специалист. Опыт работы в написании: контрольных, курсовых, дипломных работ и рефератов более 9-ти лет. Работы выполняю ответственно, в срок или даже раньше! Владею русским и украинским языками.