Even Multiple Angle Formula for Cosine

Theorem

$\ds \cos 2 n \theta = \paren {-1}^n \prod_{k \mathop = 1}^n \paren {1 - \frac {\cos^2 \theta} {\map {\cos^2} {\frac {\paren {2 k - 1} \pi} {4 n} } } }$

Proof

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Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Miscellaneous Problems: $162$