1. ## Trigonometry Identity Rearrangement

Can someone show me how $\sin ^22\theta$ equal to $1-\cos 4\theta$?

2. Hello,

Originally Posted by Air
Can someone show me how $\sin ^22\theta$ equal to $1-\cos 4\theta$?

$\cos 4 \theta=\cos (2 \cdot 2 \theta)$

Using the identity $\cos 2a=1-2 \sin^2a$, we get :

$\cos 4 \theta=1-2 \sin^2 2\theta$

$\sin^2 2 \theta=\frac{1-\cos 4 \theta}{\color{red}2}$

3. ...So if we had something like:

$\sin^2 6\theta$, would that be $\frac{1 - \cos 12 \theta}{2}$?

4. Originally Posted by Air
...So if we had something like:

$\sin^2 6\theta$, would that be $\frac{1 - \cos 12 \theta}{2}$?
Yes =)

Always refer to double angle properties ^^
It's just a matter of substitution.