Answer
See below.
Work Step by Step
$RHS=\frac{sin\theta+1}{cos\theta}=\frac{sin\theta+1}{cos\theta}\times\frac{sin\theta+cos\theta-1}{sin\theta+cos\theta-1}=\frac{sin^2\theta-1+sin\theta cos\theta+cos\theta}{cos\theta(sin\theta+cos\theta-1)}=\frac{-cos^2\theta+sin\theta cos\theta+cos\theta}{cos\theta(sin\theta+cos\theta-1)}=\frac{-cos\theta+sin\theta +1}{sin\theta+cos\theta-1}=LHS$
