Quintuple Angle Formulas
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Theorem
Quintuple Angle Formula for Sine
- $\sin 5 \theta = 5 \sin \theta - 20 \sin^3 \theta + 16 \sin^5 \theta$
Quintuple Angle Formula for Cosine
- $\cos 5 \theta = 16 \cos^5 \theta - 20 \cos^3 \theta + 5 \cos \theta$
Quintuple Angle Formula for Tangent
- $\tan 5 \theta = \dfrac {\tan^5 \theta - 10 \tan^3 \theta + 5 \tan \theta} {1 - 10 \tan^2 \theta + 5 \tan^4 \theta}$
where $\sin, \cos, \tan$ denote sine, cosine and tangent respectively.