 Double-angle formula

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