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If a and b are natural numbers and f(x)=...

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

A

`pi`

B

`2pi`

C

`2pi(sqrt(a^(2)-3)+sqrt(b^(2)+7))`

D

`pi(sqrt(a^(2)-3)+sqrt(b^(2)+7))`

Text Solution

Verified by Experts

The correct Answer is:
B
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`.
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