# Math Help - Trig Identity

1. ## Trig Identity

Prove the identity

$cot\;\frac{\alpha}{2}\;=\;\frac{1 + cos\;\alpha}{sin\;\alpha}$

Any help appreciated. I'm lost here.

2. $\sin^2 \frac{\alpha}{2} = \frac{1-\cos\alpha}{2}$

$\cos^2 \frac{\alpha}{2} = \frac{1+\cos\alpha}{2}$

$\frac{\cos^2 \frac{\alpha}{2}}{\sin^2 \frac{\alpha}{2}} = \frac{\frac{1+\cos\alpha}{2}}{\frac{1-\cos\alpha}{2}}$

$\cot^2 \frac{\alpha}{2} = \frac{1+\cos\alpha}{1-\cos\alpha}$

$\cot^2 \frac{\alpha}{2} = \frac{1+\cos\alpha}{1-\cos\alpha}\cdot\frac{1+\cos\alpha}{1+\cos\alpha}$

$\cot^2 \frac{\alpha}{2} = \frac{(1+\cos\alpha)^2}{1-\cos^2\alpha}$

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

$\cot \frac{\alpha}{2} = \frac{1+\cos\alpha}{\sin \alpha}$

3. How exactly did you get that first step?

4. Originally Posted by Vitamin
How exactly did you get that first step?
Half-angle identity.