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

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

Leave a Comment

Your email address will not be published. Required fields are marked *

BOOK

Free Class