Answer
See explanations.
Work Step by Step
Step 1. To prove the given identify, we need to prove $(sin\theta-cos\theta+1)(cos\theta)=(sin\theta+cos\theta-1)(sin\theta+1)$
Step 2. From above, we have $LHS=sin\theta cos\theta-cos^2\theta+cos\theta$
Step 3. From Step 1. we have $RHS=sin^2\theta-1+sin\theta cos\theta+cos\theta=-cos^2\theta+sin\theta cos\theta+cos\theta=LHS$
