Power Reduction Formulas/Cosine Cubed

(Redirected from Cube of Cosine)

Theorem

$\cos^3 x = \dfrac {3 \cos x + \cos 3 x} 4$

where $\cos$ denotes cosine.

Proof

 $\displaystyle \cos 3 x$ $=$ $\displaystyle 4 \cos^3 x - 3 \cos x$ Triple Angle Formula for Cosine $\displaystyle \leadsto \ \$ $\displaystyle 4 \cos^3 x$ $=$ $\displaystyle 3 \cos x + \cos 3 x$ rearranging $\displaystyle \leadsto \ \$ $\displaystyle \cos^3 x$ $=$ $\displaystyle \dfrac {3 \cos x + \cos 3 x} 4$ dividing both sides by $4$

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