We have \sin^{2n}(x)+\cos^{2n}(x) has period \pi/2 for n\in\mathbb{N}\backslash \{1\}:


 

Also \sin^{2n+1}(x)+\cos^{2n+1}(x) has period 2\pi for n\in\mathbb{N}:

 

We have \sin^{-2n}(x)+\cos^{-2n}(x) has period \pi/2 for n\in\mathbb{N}:

 

Also \sin^{-2n+1}(x)+\cos^{-2n+1}(x) has period 2\pi for n\in\mathbb{N}:

 

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