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