Question

Prove that $\frac{\text{cosec}A}{\cot A+\tan A}=\cos A$.

Answer 1

Solving LHS of $\frac{\csc A}{\cot A+\tan A}=\cos A$

$\frac{\csc A}{\cot A+\tan A}=\frac{\frac{1}{\sin A}}{\frac{\cos A}{\sin A}+\frac{\sin A}{\cos A}}$

$=\frac{1}{\sin A}\times \frac{\sin A\cos A}{{\cos }^{2}A+{\sin }^{2}A}$

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

$=\cos A$