Question

If $4{\cos }^2\theta +\sqrt{3}=2(\sqrt{3}+1)\cos \theta ,$ then $\theta$ is

• A. $2n\pi \pm \frac{\pi }{3},n\in I$
• B. $2n\pi \pm \frac{\pi }{4},n\in I$
• C. $2n\pi \pm \frac{\pi }{6},n\in I$
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A $2n\pi \pm \frac{\pi }{3},n\in I$
C $2n\pi \pm \frac{\pi }{6},n\in I$

$4{\cos }^{2}x+\sqrt{3}=2(\sqrt{3}+1)\cos x\Rightarrow \cos x=\frac{2(\sqrt{3}+1)\pm 2(\sqrt{3}-1)}{8}=\frac{\sqrt{3}}{2},\frac{1}{2}\Rightarrow x=2n\pi +\frac{\pi }{3},2n\pi +\frac{\pi }{6}$