三角関数

\sec{\theta} = \frac{1}{\cos{\theta}}

\cosec{\theta} = \csc{\theta} = \frac{1}{\sin{\theta}}

\cot{\theta} = \frac{1}{\tan{\theta}}

\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}

\sin^2{\theta} + \cos^2{\theta} = 1

\tan^2{\theta} + 1 = \frac{1}{\cos^2{\theta}}

\sin{\left(x \pm y\right)} = \sin{x}\cos{y} \pm \cos{x}\sin{y}

\cos{\left(x \pm y\right)} = \cos{x}\cos{y} \mp \sin{x}\sin{y}

\tan{\left(x \pm y\right)} = \frac{\tan{x} \pm \tan{y}}{1 \mp \tan{x}\tan{y}}

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

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

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

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

\sin{x} + \sin{y} = 2\sin{\frac{x+y}{2}}\cos{\frac{x-y}{2}}

\sin{x} - \sin{y} = 2\cos{\frac{x+y}{2}}\sin{\frac{x-y}{2}}

\cos{x} + \cos{y} = 2\cos{\frac{x+y}{2}}\cos{\frac{x-y}{2}}

\cos{x} - \cos{y} = -2\sin{\frac{x+y}{2}}\sin{\frac{x-y}{2}}