Question

$\sqrt{ \frac{1 + \sin( \alpha ) }{1 - \sin( \alpha ) } }$

Answer 1

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

Answer 2

hello frnds.
_______

seen the attachments