Prove that $\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left(\frac{\pi}{2}+x\right)}=\cot ^{2} x$

Vedclass pdf generator app on play store
Vedclass iOS app on app store

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

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

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

$=\cot ^{2} x$

$= R . H.S$

Similar Questions

If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $

If the arcs of the same lengths in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centre, find the ratio of their radii.

If $\sin \theta + {\rm{cosec}}\theta = {\rm{2}}$, then ${\sin ^2}\theta + {\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta = $

If $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma )$$ = \tan \alpha \tan \beta \tan \gamma $, then $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )$$(\sec \gamma - \tan \gamma ) = $

Prove that: $\sin 3 x+\sin 2 x-\sin x=4 \sin x \cos \frac{x}{2} \cos \frac{3 x}{2}$