Cosine of Integer Multiple of Argument/Formulation 9/Examples/Cosine of Quintuple Angle

Example of Use of Cosine of Integer Multiple of Argument/Formulation 9

 * $\map \cos {5 \theta } = \map \sin {4 \theta} \paren { -2 \sin \theta + \cfrac 1 {2 \sin \theta + \cfrac 1 {-2\sin \theta + \cfrac 1 {2 \sin \theta } }} }$

Proof
Follows directly from the Cosine of Integer Multiple of Argument/Formulation 9:

Explicit derivation illustrated below: