Question

Evaluate:
${\int }_0^{\pi /2}\frac{1}{1+\cos x}dx$.

Answer 1

${\int }_0^{\pi /2}$ $\frac{1}{1+cosx}dx.$

we know $1+cosx=2co{s}^2\frac{x}{2}$

$\frac{1}{2}{\int }_0^{\pi /2}$ $se{c}^2\frac{x}{2}dx$

$[\frac{2}{2}tan\frac{x}{2}{]}_0^{\pi /2}$ =$tan\frac{\pi }{4}$-0=1