Correct Answer - Option 2 : π

__Concept:__

For a trigonometric function, the length of one complete cycle is called a period.

In general, we have three basic trigonometric functions like sin, cos, and tan functions, having 2π, 2π, and π periods respectively.

- If a function f(x) is periodic with T , then the function f(ax + b) is periodic with \(\rm \frac{T}{|a|}\)

__Calculation:__

Given function:f(x) = 2sin x cos x = sin 2x

The period of sin function is 2π.

We know, If a function f(x) is periodic with T , then the function f(ax + b) is periodic with \(\rm \frac{T}{|a|}\)

∴ The period of sin 2x will be \(\rm \frac{2π }{2}\) = π