# Addition and Subtraction Formulas

Angles: $$\alpha$$, $$\beta$$
Trigonometric functions: $$\sin \alpha,$$ $$\cos \alpha,$$ $$\tan \alpha,$$ $$\cot \alpha$$
1. Sine addition formula
$$\sin \left( {\alpha + \beta } \right) =$$ $$\sin \alpha \cos \beta \,+$$ $$\cos \alpha \sin \beta$$
2. Sine subtraction formula
$$\sin \left( {\alpha – \beta } \right) =$$ $$\sin \alpha \cos \beta \,-$$ $$\cos \alpha \sin \beta$$
3. Cosine addition formula
$$\cos \left( {\alpha + \beta } \right) =$$ $$\cos \alpha \cos \beta \,-$$ $$\sin \alpha \sin \beta$$
4. Cosine subtraction formula
$$\cos \left( {\alpha – \beta } \right) =$$ $$\cos \alpha \cos \beta \,+$$ $$\sin \alpha \sin \beta$$
5. Tangent addition formula
$$\tan \left( {\alpha + \beta } \right) = \large\frac{{\tan \alpha + \tan \beta }}{{1 – \tan \alpha \tan \beta }}\normalsize$$
6. Tangent subtraction formula
$$\tan \left( {\alpha – \beta } \right) = \large\frac{{\tan \alpha – \tan \beta }}{{1 + \tan \alpha \tan \beta }}\normalsize$$
7. Cotangent addition formula
$$\cot \left( {\alpha + \beta } \right) = \large\frac{{1 – \tan \alpha \tan \beta }}{{\tan \alpha + \tan \beta }}\normalsize$$
8. Cotangent subtraction formula
$$\cot \left( {\alpha – \beta } \right) = \large\frac{{1 + \tan \alpha \tan \beta }}{{\tan \alpha – \tan \beta }}\normalsize$$