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