Question

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

Answer 1

LHS$=\frac{1+\cos A}{\sin A}$

Multiply and divide LHS by $(1-\cos A)$

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

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

$=\frac{\sin A}{1-\cos A}$

$=RHS$

Hence proved