Question

Find the period of $f\left(x\right)={\sin }^{4}x+{\cos }^{4}x$

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $3\pi$
• D. None of these

Answer 1

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

${\sin }^{4}x$ and ${\cos }^{4}x$ both has a period $\pi$ as $n$ is even.
But $f\left(x\right)$ is an even function and $\sin x$ and $\cos x$ are complementary.
Hence, $f\left(x\right)$ has period $=\frac{1}{2}\{\text{LCM of}\pi ,\pi \}=\frac{\pi }{2}$
Thus, period of $f\left(x\right)$ is $\frac{\pi }{2}$.