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