Question

Prove that. $\frac{cos(π+x)cos(-x)}{sin(π-x)cos(\frac{π}{2}+x)}=cot^2x$

Answer 1

$L.H.S=\frac{cos({\pi}+x)cos(-x)}{sin({\pi}-x)cos(\frac{\pi}{2}+x)}$

$=\frac{[-cos\,x][cos\,x]}{(sin\,x)(-sin\,x)}$

$\frac{-cos^2x}{-sin^2x}$

$=cot^2x$

$=R.H.S.$