Question

Show that:
$\frac{\cos A}{1+\sin A}+\tan A=\sec A$

Answer 1

To prove:- $\frac{\cos A}{1+\sin A}+\tan A=\sec A$

Proof:-

Taking l.H.S., we have

$\frac{\cos A}{1+\sin A}+\tan A$

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

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

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

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

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

$=\sec A$

$=$ R.H.S.

Hence proved.