Question

Доказать тождество :
\frac { \sin ( \pi - \alpha ) \sin ( \alpha + 2 \pi ) } { \tan ( \pi + \alpha ) \cos ( \frac { \pi } { 2 } + \alpha ) } = - \cos \alpha

Answer 1

$\dfrac{sin(\pi -a)\cdot sin(a+2\pi )}{tg(\pi +a)\cdot cos(\frac{\pi}{2}+a)}=\dfrac{sina\cdot sina}{tga\cdot (-sina)}=-\dfrac{sina}{tga}=-\dfrac{sina}{sina/cosa}=-cosa$