Triple Angle Formulas
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Theorem
Triple Angle Formula for Sine
- $\sin 3 \theta = 3 \sin \theta - 4 \sin^3 \theta$
Triple Angle Formula for Cosine
- $\cos 3 \theta = 4 \cos^3 \theta - 3 \cos \theta$
Triple Angle Formula for Tangent
- $\tan 3 \theta = \dfrac {3 \tan \theta - \tan^3 \theta} {1 - 3 \tan^2 \theta}$
where $\sin, \cos, \tan$ denote sine, cosine and tangent respectively.
Triple Angle Formula for Hyperbolic Sine
- $\sinh 3 x = 3 \sinh x + 4 \sinh^3 x$
Triple Angle Formula for Hyperbolic Cosine
- $\cosh 3 x = 4 \cosh^3 x - 3 \cosh x$
Triple Angle Formula for Hyperbolic Tangent
- $\tanh {3 x} = \dfrac {3 \tanh x + \tanh^3 x} {1 + 3 \tanh^2 x}$
where $\sinh, \cosh, \tanh$ denote hyperbolic sine, hyperbolic cosine and hyperbolic tangent respectively.