# Express sin x/2 in terms of cos x using the double angle identity

Express sin x/2 in terms of cos x using the double angle identity

### Solution

From the trigonometric identity we know that

$\cos{2}x= 1-2\sin ^{2}x$ $\cos ^{2}x= 1-2\sin ^{2}\frac{x}{2}$ $2\sin ^{2}\frac{x}{2}=1-\cos x$ $\sin ^{2}\frac{x}{2}= \frac{1-\cos x}{2}$ $\sin\frac{x}{2}= \pm \sqrt {\frac{1-\cos x}{2}}$