Question

The period of the function $f(x)={\sin }^{4}x+{\cos }^{4}x$ is:

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. $2\pi$
• D. none of these

Answer 1

Answer: (B)

$f(x)={\sin }^{4}x+{\cos }^{4}x$ $={({\sin }^{2}x+{\cos }^{2}x)}^2-2{\sin }^{2}x{\cos }^{2}x$ $=1-\frac{1}{2}{(\sin 2x)}^2=1-\frac{1}{2}\left[\frac{1-\cos 4x}{2}\right]$ $=\frac{3}{4}+\frac{1}{4}\cos 4x$ Since, $\cos x$ is periodic with period $2\pi$ $\therefore$ The period off $f(x)=\frac{2\pi }{4}=\frac{\pi }{2}$