Ask Me Help Desk - How would you prove cot theta + (sin theta/1+cos theta)= csc theta ?

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how would you prove cot theta + (sin theta/1+cos theta)= csc theta ?

This is a seatwork in my trigonometry subject. Please help

$cot\theta + \frac{sin\theta}{1+cos\theta}$

Convert everything to cos and sin.

$= \frac{cos\theta}{sin\theta} + \frac{sin\theta}{1+cos\theta}$

Combine to form a single fraction:

$= \frac{cos\theta(1+cos\theta) + sin^2\theta}{sin\theta(1+cos\theta)}$

Sinplify:

$= \frac{cos\theta + cos^2 \theta + sin^2\theta}{sin\theta(1+cos\theta)}$

Now, cos^2theta + sin^2theta = 1. So,

$= \frac{cos\theta + 1}{sin\theta(1+cos\theta)}$

Can you complete it now? :)

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