Trigonometric functions of sum and difference of two angles are useful when we need to find exact values for angles such as 15o and 75o. The sum and difference formulas for sine, cosine, tangent, and cotangent are given below.

1.
Sine of sum of angles
$\sin(\alpha+\beta)=\sin\alpha \, \cos\beta + \sin\beta \, \cos\alpha$
Trigonometry
2.
$\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\tan\beta}{\tan\alpha-\tan\beta}$
Trigonometry
3.
$\sin(\alpha - \beta) = \sin\alpha \, \cos\beta - \sin\beta\,\cos\alpha$
Trigonometry
4.
$\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$
Trigonometry
5.
$\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$
Trigonometry
6.
$\tan(\alpha+\beta)=\dfrac{\tan\alpha + \tan\beta}{1-\tan\alpha\tan\beta}$
Trigonometry
7.
$\tan(\alpha-\beta)=\dfrac{\tan\alpha - \tan\beta}{1+\tan\alpha\tan\beta}$
Trigonometry
8.
$\cot(\alpha+\beta)=\dfrac{1-\tan\alpha\tan\beta}{\tan\alpha+\tan\beta}$
Trigonometry

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