Question

Prove that $\frac{sinA}{1-cosA}=cosecA+cotA$

Answer 1

Multiply and divide by $(1+\cos A)$

$\Rightarrow \frac{\sin A(1+\cos A)}{(1-\cos A)(1+\cos A)}$

$\Rightarrow \frac{\sin A(1+\cos A)}{1-{\cos }^{2}A}$

$\Rightarrow \dfrac {\sin A (1 +\cos A)}{\sin ^{2} A} $

$\Rightarrow \frac{\sin A+\sin A\cos A}{{\sin }^{2}A}$

$=cosecA+\cot A$