Question

Cos theta by 1+sin theta =tan (π/4-theta/2

Answer 1

the answer is explained in the image.

hope it will help you.

Answer 2

$\frac{cos \theta}{ 1 + sin \theta} \\ \\ = \frac{sin( \frac{\pi}{2} - \theta)}{1 + cos( \frac{\pi}{2} - \theta) } \\ \\ = \frac{2sin \frac{ \frac{\pi}{2} - \theta }{2} cos \frac{ \frac{\pi}{2} - \theta}{2} }{2 {cos}^{2} \frac{ \frac{\pi}{2} - \theta }{2} } \\ \\ = \frac{sin( \frac{\pi}{4} - \frac{ \theta}{2} )}{cos( \frac{\pi}{2} - \frac{ \theta}{2}) } \\ \\ = tan( \frac{\pi}{2} - \frac{ \theta}{2} )$