The period of $\sin\left(2πx+\frac{π}{3}\right)+2\sin\left(3πx+\frac{π}{4}\right)\sin 5πx$ is

2 5 3 none of these

2

Period of $\sin\left(2πx+\frac{π}{3}\right)$ is 1 Period of $\sin\left(3πx+\frac{π}{4}\right)$ is $\frac{2}{3}$, Period of $\sin(5πx)$ is $\frac{2}{5}$ ∴ Required period is LCM of 1, $\frac{2}{3}$ and $\frac{2}{5}=\frac{LCM\, of\,1,2,2}{HCF\, of\,1,3,5}=\frac{2}{1}=2$