Question

Prove :

$\frac{cosA}{1-tanA}+\frac{sinA}{1-cotA}=cosA+sinA$

Answer 1

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

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

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

$=\cos A+\sin A$

Hence proved.