Question

Prove that
✓1+sin /1-sin=sec +tan​

Answer 1

Step-by-step explanation:

$\sqrt{ \frac{1 + \sin( \alpha ) }{1 - \sin( \alpha ) } } \\ = \: \sqrt{ \frac{(1 + \sin( \alpha ) )(1 + \sin(\alpha )) }{(1 - \sin( \alpha ) )(1 + \sin( \alpha )) } } \\ = \: \sqrt{ \frac{ {(1 + \sin( \alpha ) })^{2} }{1 - { \sin( \alpha ) }^{2} } } \\ = \: \sqrt{ \frac{ {(1 + \sin( \alpha ) )}^{2} }{ { \cos( \alpha ) }^{2} } } \\ = \: \frac{1 + \sin( \alpha ) }{ \cos( \alpha ) } \\ = \: \frac{1}{ \cos( \alpha ) } + \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ = \: \sec( \alpha ) + \tan( \alpha )$

hence proved