Question

Prove that:

$\frac{\cos ecA-1}{\cos ecA+1}={\left[\frac{\cos A}{1+\sin A}\right]}^2$

Answer 1

Solution :-

$\frac{cosecA-1}{cosecA+1}$

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

$=\frac{1-si{n}^{2}A}{(1+sinA{)}^2}$

$=\frac{co{s}^{2}A}{(1+sinA{)}^2}$

$={\left(\frac{cosA}{1+sinA}\right)}^2$