Question

Prove that: $\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=\cos A+\sin A$

Answer 1

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

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

$=\frac{co{s}^{2}A}{cosA-sinA}+\frac{si{n}^{2}A}{sinA-coaA}$

$=\frac{co{s}^{2}A-si{n}^{2}A}{cosA-sinA}$

$=cosA+sinA$

Hence , Proved.