Question

Найдите значение выражения:
cos (3Pi-B) - sin (- 3Pi/2 + B) / 5 cos (B - Pi)

Answer 1

Ответ:

$\cos(3\pi - x) = - \cos(x) \\ \sin( - \binom{3\pi}{2} + x ) = \\ = \sin( - (\binom{3\pi}{2} - x) ) = \\ - \sin( \binom{3\pi}{2} - x ) = \cos(x) \\ \cos(x - \pi) = \cos( - (\pi - x)) = \\ = \cos(\pi - x) = - \cos(x) \\ \\ \frac{ \cos(3\pi - x) - \sin( - \binom{3\pi}{2} + x )}{5 \cos(x - \pi)} = \\ = \frac{ - \cos(x) - \cos(x) }{5( - \cos(x)) } = \\ \frac{ - 2 \cos(x) }{ - 5 \cos(x) } = \frac{2}{5}$