Question

Prove that $\frac{\cos A}{1-\sin A}+\frac{\cos A}{1+\sin A}=2\sec A$.

Answer 1

L.H.S $=\frac{\cos A}{1-\sin A}+\frac{\cos A}{1+\sin A}$

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

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

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

$=2\sec A$

$=$ R.H.S

Hence proved.