Question

The function has period $\ast {\sin }^{4}x+{\cos }^{4}x$

• A. $\pi /2.$
• B. $\pi /4.$
• C. $\pi .$
• D. $2\pi .$

Answer 1

The correct option is A $\pi /2.$

$\ast {\sin }^{4}x+{\cos }^{4}x={({\sin }^{2}x+{\cos }^{2}x)}^2-2{\sin }^{2}x{\cos }^{2}x$ $=1-\frac{1}{2}{\sin }^{2}2x$ $=1-\frac{1}{4}(1-\cos 4x)=\frac{3}{4}+\frac{1}{4}\cos 4x.$

Since the function $\cos 4x$ has period $=2\pi /4=\pi /2,$ the given function also has period $\pi /2.$