Question

prove the following trigonometry identity.

Answer 1

RHS=
$\frac{sin {}^{2} \alpha }{1 - cos \alpha } \\ \frac{1 - cos {}^{2} \alpha }{1 - cos \alpha } \\ \frac{1 - cos \alpha (1 + cos \alpha )}{1 - cos \alpha } \\ cancellation \: of \: 1 - cos \alpha \\ 1 +cos \alpha \\ 1 + \frac{1}{sec \alpha } \\ \frac{1 + sec \alpha }{sec \alpha }$