User:T-9000/Files/Mathematics & Science/Mathematics/TrigForms1

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
$$\sin (2 \cdot x) = 2 \cdot \sin (x) - \cos (x)$$ $$\begin{align} \cos(2 \cdot x) & = \cos^2(x) - \sin^2(x) \\ & = 1 - 2 \cdot \sin^2(x) \\ & = 2 \cdot \cos^2(x) - 1 \\ \end{align}$$ $$\tan(2 \cdot x) = \frac {2 \cdot \tan(x)} {1 - \tan^2(x)}$$ $$\cot(2 \cdot x) = \frac {\cot^2(x) - 1} {2 \cdot \cot(x)}$$

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