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Algebra Level 4

\( S=1+\frac { \cos { x } }{ \cos { x } } +\frac { \cos { 2x } }{ \cos ^{ 2 }{ x } } +\cdots+\frac { \cos { nx } }{ \cos ^{ n }{ x } } \\ { S }^{ ' }=\frac { \sin { x } }{ \cos { x } } +\frac { \sin { 2x } }{ \cos ^{ 2 }{ x } } +\cdots +\frac { \sin { nx } }{ \cos ^{ n }{ x } } \\ S=?\)

Use \(S'\) to find \(S\).

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