Power Reduction Formulas/Hyperbolic Cosine Squared/Proof 3

Theorem

$\cosh^2 x = \dfrac {\cosh 2 x + 1} 2$

Proof

\(\ds \cosh^2 x\)

\(=\)

\(\ds \cos^2 i x\)

Hyperbolic Cosine in terms of Cosine

\(\ds \)

\(=\)

\(\ds \frac {\map \cos {2 i x} + 1} 2\)

Square of Cosine

\(\ds \)

\(=\)

\(\ds \frac {\cosh 2 x + 1} 2\)

Hyperbolic Cosine in terms of Cosine

$\blacksquare$