Question

СРОЧНО
упростите выражение:
(1-cosx)(1+cosx)/sinx+sin(π-x)-tgxcosx(π+x)/2

Answer 1

Ответ:

$\frac{(1 - \cos(x))(1 + \cos(x)) }{ \sin(x) + \sin(\pi - x) } - \frac{tgx \times \cos(\pi + x) }{2} = \\ = \frac{1 - \cos {}^{2} (x) }{ \sin(x) + \sin(x) } - \frac{1}{2} tgx \times ( - \cos(x)) = \\ = \frac{ \sin {}^{2} (x) }{2 \sin(x) } + \frac{1}{2} \times \frac{ \sin(x) }{ \cos(x) } \times \cos(x) = \\ = \frac{1}{2} \sin(x) + \frac{1}{2} \sin(x) = \sin(x)$