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