Question

prove that cos theta/1-sin theta = 1+ sin theta/ cos theta​

Answer 1

Answer:

$\frac{ \cos( \alpha ) }{1 + \sin( \alpha ) } = \frac{1 - \sin( \alpha ) }{ \cos( \alpha ) } \\ ls = \frac{ \cos( \alpha ) }{1 + \sin( \alpha ) }. \frac{1 - \sin( \alpha ) }{1 - \sin( \alpha )} \\ = \frac{ \cos( \alpha ) (1 - \sin( \alpha ))}{1 - { \sin }^{2}( \alpha ) } \\ = \frac{ \cos( \alpha)(1 - \sin( \alpha ) }{ { \cos}^{2} (\alpha ) } \\ = \frac{1 - \sin( \alpha ) }{ \cos( \alpha ) }$

$let \: theta \: be \: = \alpha$