Question

The complete solution set of $\sin x-\sqrt{3}\cos x=0$ is

• A. $n\pi -\frac{\pi }{3}$
• B. $n\pi \pm \frac{\pi }{3}$
• C. $n\pi +\frac{\pi }{3}$
• D. $n\pi \pm \frac{\pi }{6}$

Answer 1

The correct option is C $n\pi +\frac{\pi }{3}$

$\sin x-\sqrt{3}\cos x=0\Rightarrow \sin x=\sqrt{3}\cos x\Rightarrow \tan x=\sqrt{3}\therefore x=n\pi +\frac{\pi }{3}$