Double Angle Identities

Sine:

 \sin(2\theta) = 2\sin\theta\cos\theta

Cosine:


\begin{matrix}
\cos(2\theta) = \cos^2\theta - \sin^2\theta\\
= 1 - 2sin^2\theta\\
= 2cos^2\theta - 1\\
\end{matrix}

Tan:

 \tan(2\theta) = \dfrac{2\tan\theta}{1-\tan^2\theta}

Half Angle Identities

Whether the output is positive or negative depends on what quadrant the output is in. Sine:

 \sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{2}}

Cosine:

 \cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos\theta}{2}}

Tangent:

 \tan(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{1 + \cos\theta}}