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Q.
If $f (x) = \sin^6 \, x + \cos^6 \, x,$ then the period of the function f (x) is
Trigonometric Functions
Solution:
Here $f \left(\frac{ \pi}{2}+x\right) = \sin^{6} \left(\frac{\pi}{2}+x\right) + \cos^{6} \left(\frac{\pi}{2} +x\right)$
$ = \cos^{6} x + \sin^{6} x =f \left(x\right)$ for all x,