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Compound Angle Formulas

$\sin(x+y)=\sin(x)\times \cos(y)+\cos(x)\times \sin(y)\,\!$

$\sin(x-y)=\sin(x)\times \cos(y)-\cos(x)\times \sin(y)\,\!$

$\cos(x+y)=\cos(x)\times \cos(y)-\sin(x)\times \sin(y)\,\!$

$\cos(x-y)=\cos(x)\times \cos(y)+\sin(x)\times \sin(y)\,\!$

$\tan(x+y)={\frac {\tan(x)+\tan(y)}{1-\tan(x)\times \tan(y)}}$

$\tan(x-y)={\frac {\tan(x)-\tan(y)}{1-\tan(x)\times \tan(y)}}$

$\cot(x+y)={\frac {\cot(x)\times \cot(y)-1}{\cot(x)+\cot(y)}}$

$\cot(x-y)={\frac {\cot(x)\times \cot(y)+1}{\cot(y)-\cot(x)}}$

Double Angle Formulas

$\sin(2\cdot x)=2\cdot \sin(x)-\cos(x)$

${\begin{aligned}\cos(2\cdot x)&=\cos ^{2}(x)-\sin ^{2}(x)\\&=1-2\cdot \sin ^{2}(x)\\&=2\cdot \cos ^{2}(x)-1\\\end{aligned}}$

$\tan(2\cdot x)={\frac {2\cdot \tan(x)}{1-\tan ^{2}(x)}}$

$\cot(2\cdot x)={\frac {\cot ^{2}(x)-1}{2\cdot \cot(x)}}$

Sum and Difference Formulas

$\sin(x)+\sin(y)=2\cdot \sin \left({\frac {x+y}{2}}\right)\cdot \cos \left({\frac {x-y}{2}}\right)$

$\sin(x)-\sin(y)=2\cdot \cos \left({\frac {x+y}{2}}\right)\cdot \sin \left({\frac {x-y}{2}}\right)$

$\cos(x)+\cos(y)=2\cdot \cos \left({\frac {x+y}{2}}\right)\cdot \cos \left({\frac {x-y}{2}}\right)$

$\cos(x)-\cos(y)=-2\cdot \sin \left({\frac {x+y}{2}}\right)\cdot \sin \left({\frac {x-y}{2}}\right)$

Product Formulas

$\sin(x)\cdot \cos(y)={\frac {1}{2}}\cdot \left(\sin(x+y)+\sin(x-y)\right)$

$\sin(x)\cdot \sin(y)=-{\frac {1}{2}}\left(\cos(x+y)-\cos(x-y)\right)$

$\cos(x)\cdot \cos(y)={\frac {1}{2}}\left(\cos(x+y)+\cos(x-y)\right)$