$\sin^{2} {x} +\cos^{2} {x}=1$
$\tan^{2} {x} + 1 = \sec^{2} {x}$
$ 1 + \cot^{2} {x} = \csc^{2} {x}$
$\sin (\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta$
$\cos (\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta$
$\tan (\alpha \pm \beta) = \frac { \tan \alpha \pm \tan \beta} {1 \mp \tan \alpha \tan \beta}$
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