Question

The least value of x for $0<x<\frac{\pi }{2}$, such that $\cos \left(2x\right)=\sqrt{3}\sin \left(2x\right)$, is

• A. $\frac{\pi }{12}$
• B. $\frac{2\pi }{12}$
• C. $\frac{3\pi }{12}$
• D. $\frac{4\pi }{12}$

Answer 1

The correct option is A $\frac{\pi }{12}$

Given $\cos 2x=\sqrt{3}\sin 2x$
$\Rightarrow \tan 2x=\frac{1}{\sqrt{3}}$
hence general solution is,
$2x=k\pi +\frac{\pi }{6}$, where $k$ is any integer
$\Rightarrow x=\frac{k\pi }{2}+\frac{\pi }{12}$
so least value of $x$ for $0<x<\frac{\pi }{2}$ is, $x=\frac{\pi }{12}$