Question

please find the answer for this question​

Answer 1

Step-by-step explanation:

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