Question
Prove the following identities.$$2 \sin ^{2} \frac{\theta}{2}=\frac{\sin ^{2} \theta}{1+\cos \theta}$$.
Step 1
The half angle formula for sine is $\sin^2(\frac{\theta}{2}) = \frac{1 - \cos(\theta)}{2}$. So, we have $2 \sin^2(\frac{\theta}{2}) = 2 \cdot \frac{1 - \cos(\theta)}{2}$. Show more…
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