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Trigonometry - Addition and subtraction formulas

\(sin(\alpha+\beta)=sin\alpha.cos\beta+sin\beta.cos\alpha\)
\(sin(\alpha-\beta)=sin\alpha.cos\beta-sin\beta.cos\alpha\)
\(cos(\alpha+\beta)=cos\alpha.cos\beta-sin\alpha.sin\beta\)
\(cos(\alpha-\beta)=cos\alpha.cos\beta+sin\alpha.sin\beta\)
\(tan(\alpha+\beta)={{tan\alpha+tan\beta} \over 1-tan\alpha.tan\beta}\)
\(tan(\alpha-\beta)={{tan\alpha-tan\beta} \over 1+tan\alpha.tan\beta}\)
\(cot(\alpha+\beta)={ 1-tan\alpha.tan\beta \over {tan\alpha+tan\beta} }\)
\(cot(\alpha-\beta)={ 1+tan\alpha.tan\beta \over {tan\alpha-tan\beta} }\)