Question

Solve this Find the value of a

Answer 1

Hey

$\frac{1}{1 + \sin(x) } = \frac{1}{2 \cos {}^{2} ( \frac{x}{2} - \frac{\pi}{4} ) } = 0.5\sec {}^{2} ( \frac{x}{2} - \frac{\pi}{4} )$

Assuming the value ( above )

$\frac{1}{2} \int \sec {}^{2} ( \frac{x}{2} - \frac{\pi}{4} ) dx$

-> which has the integral :

$\tan( \frac{x}{2} - \frac{\pi}{4} ) + c$

where, C a constant belongs to the set of real numbers

=> Option (A)