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