Can someone show me how $\displaystyle \sin ^22\theta$ equal to $\displaystyle 1-\cos 4\theta$? Thanks in advance.
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Hello, Originally Posted by Air Can someone show me how $\displaystyle \sin ^22\theta$ equal to $\displaystyle 1-\cos 4\theta$? Thanks in advance. $\displaystyle \cos 4 \theta=\cos (2 \cdot 2 \theta)$ Using the identity $\displaystyle \cos 2a=1-2 \sin^2a$, we get : $\displaystyle \cos 4 \theta=1-2 \sin^2 2\theta$ $\displaystyle \sin^2 2 \theta=\frac{1-\cos 4 \theta}{\color{red}2}$
...So if we had something like: $\displaystyle \sin^2 6\theta$, would that be $\displaystyle \frac{1 - \cos 12 \theta}{2}$?
Originally Posted by Air ...So if we had something like: $\displaystyle \sin^2 6\theta$, would that be $\displaystyle \frac{1 - \cos 12 \theta}{2}$? Yes =) Always refer to double angle properties ^^ It's just a matter of substitution.
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