Question

What is the value of period of $2\sin x\cos x$?

Answer 1

Find the value of period of $2\sin x\cos x$.

Given: The function is $2\sin x\cos x$.

Here, $y=\sin 2x$.

We know that the period of $\sin ax$ is $\frac{2\mathrm{\pi }}{a}$.

The period of $\begin{array}{rcl}\sin 2x& =& \frac{2\pi }{2}\end{array}$
$\begin{array}{rcl}& =& \pi \end{array}$
Thus, the period of $2\sin x\cos x$ is $\mathrm{\pi }$.