# Double Angle Formulas

## Theorem

### Double Angle Formula for Sine

$\sin 2 \theta = 2 \sin \theta \cos \theta$

### Double Angle Formula for Cosine

$\cos 2 \theta = \cos^2 \theta - \sin^2 \theta$

### Double Angle Formula for Tangent

$\map \tan {2 \theta} = \dfrac {2 \tan \theta} {1 - \tan^2 \theta}$

where $\sin, \cos, \tan$ denote sine, cosine and tangent respectively.

### Double Angle Formula for Hyperbolic Sine

$\sinh 2 x = 2 \sinh x \cosh x$

### Double Angle Formula for Hyperbolic Cosine

$\cosh 2 x = \cosh^2 x + \sinh^2 x$

### Double Angle Formula for Hyperbolic Tangent

$\tanh 2 x = \dfrac {2 \tanh x} {1 + \tanh^2 x}$

where $\sinh, \cosh, \tanh$ denote hyperbolic sine, hyperbolic cosine and hyperbolic tangent respectively.