Question

The period of the function $f\left(x\right)=3\sin 2\sqrt{3}x+2\cos 5\sqrt{3}x$ is

• A. $2\pi$
• B. $\frac{2\pi }{\sqrt{3}}$
• C. $\frac{\pi }{\sqrt{3}}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is B $\frac{2\pi }{\sqrt{3}}$

Period of $3\sin 2\sqrt{3}x$ is:
$T_1=\frac{2\pi }{2\sqrt{3}}$

Period of $2\cos 5\sqrt{3}x$ is:
$T_2=\frac{2\pi }{5\sqrt{3}}$

Hence, period of given function is:
$L.C.M(\frac{2\pi }{2\sqrt{3}},\frac{2\pi }{5\sqrt{3}})=\frac{\text{LCM of}(2\pi ,2\pi )}{\text{HCF of}(2\sqrt{3},5\sqrt{3})}=\frac{2\pi }{\sqrt{3}}$