Question

prove that 1 + cos theta + sin theta upon 1 + cos theta minus sin theta is equals to 1 + sin theta upon cos theta

Answer 1

HELLO DEAR,

$\frac{1 + \cos \alpha + \sin \alpha }{1 + \cos \alpha - \sin \alpha } \\ = > \frac{ \cos \alpha (1 + \cos \alpha + \sin \alpha ) }{ \cos \alpha (1 + \cos \alpha - \sin \alpha ) } \\ = > \frac{( \cos\alpha + \cos ^{2} \alpha + \cos \alpha \sin \alpha ) }{ \cos \alpha (1+ \cos \alpha - \sin \alpha ) } \\ = > \frac{( \cos\alpha +1 - \sin ^{2} \alpha + \cos \alpha \sin \alpha ) }{ \cos \alpha (1+ \cos \alpha - \sin \alpha ) } \\ = > \frac{ (1 + \sin\alpha ) (1 - \sin \alpha ) + \cos \alpha (1 + \sin \alpha ) }{ \cos \alpha (1 + \cos \alpha - \sin \alpha ) } \\ = > \frac{(1 + \sin \alpha )(1 - \sin \alpha + \cos \alpha ) }{ \cos \alpha (1 - \sin \alpha + \cos \alpha) } \\ = > \frac{1 + \sin \alpha }{ \cos \alpha }$
I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

solution is in this attachment.

hope it helps you !!

@Rajukumar111