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Mathematics

Trigonometry

Double and Half-Angle Formulas

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Double-Angle Formula for Sine

$\sin(2x) = 2\sin(x)\cos(x)$

Double-Angle Formula for Cosine (Sum)

$\cos(2x) = \cos^2(x) - \sin^2(x)$

Double-Angle Formula for Cosine (Cosine Only)

$\cos(2x) = 2\cos^2(x) - 1$

Double-Angle Formula for Cosine (Sine Only)

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

Double-Angle Formula for Tangent

$\tan(2x) = \frac{2\tan(x)}{1 - \tan^2(x)}$

Half-Angle Formula for Sine

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

Half-Angle Formula for Cosine

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

Half-Angle Formula for Tangent

$\tan(\frac{x}{2}) = \pm\sqrt{\frac{1 - \cos(x)}{1 + \cos(x)}}$ or $\tan(\frac{x}{2}) = \frac{\sin(x)}{1 + \cos(x)}$ or $\tan(\frac{x}{2}) = \frac{1 - \cos(x)}{\sin(x)}$

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