Question

(sin(pi - a) - cos(pi/2 + a))/(cos(pi + a))

Answer 1

По формулам привидения:

$\sin(\pi - a) = \sin(a)$

$\cos(\frac{\pi}{2} + a) = -\sin(a)$

$\cos(\pi + a) = -\cos(a)$

Итак,

$\frac{\sin(\pi - a) - \cos(\frac{\pi}{2} + a)}{\cos(\pi+a)} =$

$= \frac{\sin(a) + \sin(a)}{-\cos(a)} = -2\cdot\frac{\sin(a)}{\cos(a)} = -2\mathrm{tg}(a)$