Question

Prove that
cosec theta + cottheta =sintheta / 1-cosec ​

Answer 1

Answer:

$\cosec ( \alpha ) + \cot( \alpha ) = \frac{ \sin( \alpha ) }{1 - \cosec( \alpha ) } \\ lhs \: \cosec( \alpha ) + \cot( \alpha ) \\ = \frac{1}{ \sin( \alpha ) } + \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ = \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) }$