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$\sin (\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta$
$\sin (\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta$
$\cos (\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$
$\cos (\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$
$\tan (\alpha+\beta)= \frac{ \tan \alpha + \tan \beta}{1- \tan\alpha \tan\beta}$
$\tan (\alpha-\beta)= \frac{ \tan \alpha - \tan \beta}{1+ \tan\alpha \tan\beta}$
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