Question

prove that lhs =rhs for cos theta by 1-sin theta = 1 + sin theta by cos theta

Answer 1

$\textsf{LHS}\\\\\\\dfrac {\cos\theta}{1-\sin\theta}\\\\\\\dfrac {\cos\theta (1+\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}\\\\\\\dfrac {\cos\theta (1+\sin\theta)}{1-\sin^2\theta}\\\\\\\dfrac {\cos\theta (1+\sin\theta)}{\cos^2\theta}\\\\\\\dfrac {1+\sin\theta}{\cos\theta}\\\\\\\textsf{RHS}$

$\Large\textsc{Hence Proved!}$