Question

If $f(x)={\sin }^{6}x+{\cos }^{6}x,$ then the period of the function f (x) is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $2\pi$

Answer 1

Answer: (B)

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,