Question

cos theta/1+sin theta​

Answer 1

Answer:

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