Prove that:
(a) `(sin 2 theta)/(1+cos 2 theta)=tan theta` (b) `(1+sin 2 theta+cos 2theta)/(1+sin2 theta-cos 2 theta)=cot theta`

Explanation

To prove the two given equations, we will follow a systematic approach using trigonometric identities.

### Part (a): Prove that \(\frac{\sin 2\theta}{1 + \cos 2\theta} = \tan \theta\)

**Step 1: Use the double angle identities.**
We know that:
\[
\sin 2\theta = 2 \sin \theta \cos \theta
...