Question

if $sinx+\sqrt{3}cosx=\sqrt{2}$ then x is

• A.
• B.
• C.
• D. 2nπ+π/2, nϵ Z

Answer 1

The correct option is B

$\frac{\sqrt{3}}{2}cosx+\frac{1}{2}sinx=\frac{\sqrt{2}}{2}$
$cos(x-\frac{\pi }{6})=cos\frac{\pi }{4}\Rightarrow x-\frac{\pi }{6}=2n\pi \pm \frac{\pi }{4}$
$\Rightarrow x=2n\pi \pm \frac{\pi }{4}+\frac{\pi }{6}\Rightarrow x=2n\pi +\frac{5\pi }{12},2n\pi -\frac{\pi }{12},n\in Z$