The solution set of $x\in \left(-\pi ,\pi \right)$ for the inequality $\sin 2x+1\le \cos x+2\sin x$ is

• A

  $x\in \left[0,\frac{\pi }{6}\right]$
• Correct answer
  B

  $x\in \left[\frac{\pi }{6},\frac{5\pi }{6}\right]\cup \left\{0\right\}$
• C

  $x\in \left[-\frac{\pi }{6},\frac{5\pi }{6}\right]$
• D

  $x\in \left[-\frac{\pi }{2},\frac{\pi }{2}\right]$

Hence, the correct answer is option: 'B'.