Cosine of Integer Multiple of Argument/Formulation 8/Examples/Cosine of Quintuple Angle

Example of Use of Cosine of Integer Multiple of Argument/Formulation 8

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

Proof
Follows directly from the Cosine of Integer Multiple of Argument/Formulation 8:

Explicit derivation illustrated below: