Double-angle formula
= Double-angle formula
{title2=$\sin2x=2\sin x\cos x$}
The angle-addition identities give $\sin2x=2\sin x\cos x$, $\cos2x=\cos^2x-\sin^2x=1-2\sin^2x=2\cos^2x-1$, and $\tan2x=2\tan x/(1-\tan^2x)$ wherever the <tangent> expressions are defined. The <sine> formula converts $\sin^2x\cos^2x$ into $\sin^2(2x)/4$, which is useful for trigonometric inequalities and <integration>.