Question

Prove that:
$\tan A-\cot A=-2\cot 2A$

Answer 1

L.H.S$=\tan A-\cot A$

$=\frac{\sin A}{\cos A}-\frac{\cos A}{\sin A}$

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

$=\frac{-2({\cos }^{2}A-{\sin }^{2}A)}{2\sin A\cos A}$

$=\frac{-2\cos 2A}{\sin 2A}$

$=-2\cot 2A$

$=R.H.S$

Hence proved.