Question

Помогите решить пример. Спасибо.

Answer 1

$8\sin^4(\frac{a}{2}) + 4\cos(a) - \cos(2a) = V$

$\cos(a) = 1 - 2\sin^2(\frac{a}{2})$

$\sin^2(\frac{a}{2}) = \frac{1-\cos(a)}{2}$

$\cos(2a) = \cos^2(a) - \sin^2(a) = 2\cos^2(a) - 1$

$V = 8\cdot (\frac{1-\cos(a)}{2})^2 + 4\cos(a) - (2\cos^2(a) - 1) =$

$= 8\cdot \frac{(1-\cos(a))^2}{4} + 4\cos(a) - 2\cos^2(a) + 1 =$

$= 2\cdot (1 - 2\cos(a) + \cos^2(a) ) + 4\cos(a) - 2\cos^2(a) + 1 =$

$= 2 - 4\cos(a) + 2\cos^2(a) + 4\cos(a) - 2\cos^2(a) + 1 =$

$= 2 + 1 = 3$.

Ответ. 3.