Question

Prove that
$\tan A+\cot A=2cosec2A$

Answer 1

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

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

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

$=\frac{1}{\sin A\cos A}$

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

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

$=2\csc 2A$