Question

Докажите,, тождество! заранее,. фото во вложении

Answer 1

$\frac{tg(\frac{3\pi}{2}-a)\cdot cos(\frac{3\pi}{2}-a)}{cos(2\pi -a)}+cos(a-\frac{\pi }{2})\cdot sin(\pi -a)+cos(\pi +a)\cdot sin(a-\frac{\pi}{2})=\\\\=\frac{ctga\cdot (-sina)}{cosa}+sina\cdot sina+(-cosa)\cdot (-cosa)=\\\\=\frac{-cosa}{cosa}+(sin^2a+cos^2a)=-1+1=0\\\\0=0\\\\\\\star cos(a-\frac{\pi}{2})=cos(\frac{\pi}{2}-a)=sina\; \; \star \\\\\star \; \; sin(a-\frac{\pi}{2})=-sin(\frac{\pi}{2}-a)=-cosa\; \; \star \\\\\star \; \; ctga=\frac{cosa}{sina}\; \; \star$