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What is the period of the function f(x) = 2sin x cos x?
1. 2π 
2. π 
3. 3π 
4. None of these

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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

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