Question

If$\tan A+\cot A=m\text{cosec}2A$.Find $m$

Answer 1

$If\tan A+\cot A=m\csc 2ALHS\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A}\frac{{\sin }^{2}A+{\cos }^{2}A}{\sin A\cos A}\frac{1}{\sin A\cos A}\frac{2}{2\sin A\cos A}\frac{2}{\sin 2A}2\csc 2A\therefore ComparingLHS\&RHS2\csc 2A=m\csc 2A\therefore m=2$