Question

Solve $\frac{1+\sin A}{\cos A}+\frac{\cos A}{1+\sin A}=2\sec A$

Answer 1

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

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

$=\frac{1+{\sin }^{2}A+{\cos }^{2}A+2\sin A}{\cos A(1+\sin A)}$ ............ $[sin²\theta +cos²\theta =1]$

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

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

$=\frac{2}{\cos A}=2\sec A=$R.H.S