Question

The period of $\sin (2\pi x+a)$ $\sin (2\pi x+b)$ is

• A. $\frac{a}{b}$
• B. $1$
• C. $2$
• D. $\pi$

Answer 1

Answer: (B)

$1$

$\sin (2\pi x+a)\sin (2\pi x+b)=[\sin 2\pi x.\cos a+\cos 2\pi x\sin a]\times [\sin 2\pi x+\cos b+\cos 2\pi x\sin b]$

Here, period of $\sin 2\pi x.\cos 2\pi x=1$ and $\cos a,\cos b,\sin a,\sin b$ are constant, therefore period of given function is $1$