Useful trigonometry equalities

Posted September 25th, 2007 by Isoscel

$\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta$
$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta$

$\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$
$\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$

$\sin x+\sin y=2\sin \frac{x+y}{2}\cos \frac{x-y}{2}$

$\sin x-\sin y=2\sin \frac{x-y}{2}\cos \frac{x+y}{2}$

$\cos x+\cos y =2\cos \frac{x+y}{2}\cos \frac{x-y}{2}$

$\cos x-\cos y =-2\sin\frac{x+y}{2}\sin \frac{x-y}{2}$

$\sin 2x=2\sin x\cos x$
$\cos 2x=\cos^2 x-\sin^2 x=2\cos^2 x-1=1-2\sin^2 x$

$\sin 3x=3\sin x-4\sin^3 x$
$\cos 3x=4\cos^3 x-3\cos x$

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