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