Answer
See explanations below.
Work Step by Step
We are given $sin^2\theta+cos^2\theta=1$
(a) Divide both sides by $cos^2\theta$, we have $\frac{sin^2\theta}{cos^2\theta}+1=\frac{1}{cos^2\theta}$ which gives $tan^2\theta+1=sec^2\theta$
(b) Divide both sides by $sin^2\theta$, we have $1+\frac{cos^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}$ which gives $1+cot^2\theta=csc^2\theta$
