Addition & Double Angle Formulae

Addition and double angle formulas for various trig and hyperbolic functions

Trigonometric Functions §

$\cos (x+y)=\cos (x)\cos (y)-\sin (x)\sin (y)$ $\sin (x+y)=\sin (x)\cos (y)+\cos (x)\sin (y)$

$\cos (2x)={\cos }^2(x)-{\sin }^2(x)$ $\cos (2x)=2{\cos }^2(x)-1$ $\cos (2x)=1-2{\sin }^2(x)$ $\sin (2x)=2\sin (x)\cos (x)$

Hyperbolic Functions §

$\cosh (x+y)=\cosh (x)\cosh (y)+\sinh (x)\sinh (y)$ $\sinh (x+y)=\sinh (x)\cosh (y)+\cosh (x)\sinh (y)$

$\cosh (2x)={\cosh }^2(x)+{\sinh }^2(x)$ $\cosh (2x)=2{\cosh }^2(x)-1$ $\cosh (2x)=1+2{\sinh }^2(x)$ $\sinh (2x)=2\sinh (x)\cosh (x)$