Question

Find the general solutions of $2co{s}^{2}x+\sqrt{3}cosx=0$

• A. $x=n\pi$
• B. $x=2n\pi \pm \frac{\pi }{2}$
• C. $x=2n\pi \pm \frac{5\pi }{6}$
• D. $x=2n\pi \pm \frac{\pi }{6}$

Answer 1

The correct option is C

$x=2n\pi \pm \frac{5\pi }{6}$

$2co{s}^{2}x+\sqrt{3}cosx=0cosx(2cosx+\sqrt{3})=0cosx=0orcosx=-\frac{\sqrt{3}}{2}x=2n\pi \pm \frac{\pi }{2}orx=2n\pi \pm \frac{5\pi }{6}$