Question

If $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=m\text{cosec}A.$ Find $m$.

Answer 1

Since, $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=mcosecA$

$⟹\frac{{\sin }^{2}A+1+2\cos A+{\cos }^{2}A}{(1+\cos A)\sin A}=mcosecA$

$⟹\frac{2+2\cos A}{(1+\cos A)\sin A}=mcosecA$

$⟹\frac{2}{\sin A}=mcosecA$

$⟹2\times cosecA=mcosecA$

$⟹2=m$