Question

If $f\left(x\right)=\cos 8\pi x+\sin 2\pi x\cdot \text{cosec}2\pi x$ , then fundamental period of $f\left(x\right)$ is

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $\frac{7}{8}$

Answer 1

The correct option is A $\frac{1}{4}$

$f\left(x\right)=\cos 8\pi x+\sin 2\pi x\cdot \text{cosec}2\pi x=\cos 8\pi x+1,x\ne n\pi$
$\Rightarrow f\left(x\right)=2{\cos }^{2}4\pi x$
We know, Period of ${\cos }^{2}x$ is $\pi$
$\therefore$ Period of $f\left(x\right)$ is $\frac{\pi }{4\pi }=\frac{1}{4}$