Power Reduction Formulas/Cosine Cubed

Theorem

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

where $\cos$ denotes cosine.

$\ds \cos 3 x$

$=$

$\ds 4 \cos^3 x - 3 \cos x$

$\ds \leadsto \ \ $

$\ds 4 \cos^3 x$

$=$

$\ds 3 \cos x + \cos 3 x$

rearranging

$\ds \leadsto \ \ $

$\ds \cos^3 x$

$=$

$\ds \dfrac {3 \cos x + \cos 3 x} 4$

dividing both sides by $4$

$\blacksquare$

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: $5.56$