If a and b are natural numbers and `f(x)=sin(sqrt(a^2-3))x+cos(sqrt(b^2+7))x` is periodic with finite fundamental period then period of f(x) is

Options

A. `pi`
B. `2pi`
C. `2pi(sqrt(a^(2)-3)+sqrt(b^(2)+7))`
D. `pi(sqrt(a^(2)-3)+sqrt(b^(2)+7))`

Answer

B

Explanation

Since the function is periodic, `a^(2)-3 and b^(2)+7` should be perfect square, which is possible only if a = 2, b = 3 in which case `f(x) = sin x +cos 4x`, which has periodic with `2pi`.