Question

Period of ${\cos }^{6}x+{\sin }^{6}x$ is

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

Answer 1

The correct option is A $\frac{\pi }{2}$

By, Fundamental Properties of $f\left(x\right)$ periodic function with Period T.
$f(x+T)=f\left(x\right)$
Let $f\left(x\right)={\cos }^{6}x+{\sin }^{6}x.$
assume from option smallest period of $f\left(x\right)=\pi /2$
$\therefore f(x+\pi /2)=f\left(x\right)$
$\therefore {\sin }^6(x+\pi /2)+{\cos }^6(x+\pi /2)={\cos }^{6}x+{\sin }^{6}x.$
This shows that $\frac{\pi }{2}$ is a fundamental period of $f\left(x\right)$.