If 2sin⁡x−1≤0 and x∈[0,2π]. then the solution set for x, is

# If and then the solution set for $x$, is

1. A

$\left[\pi /6,5\pi /6\right]$

2. B

$\left[0,\pi /6\right]\cup \left[5\pi /6,\pi \right]$

3. C

$\left[0,\pi /6\right]\cup \left[5\pi /6,2\pi \right]$

4. D

none of these.

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### Solution:

It is  from the graph of $y=\mathrm{sin}x$ that

for all $x\in \left[0,\pi /6\right]\cup \left[5\pi /6,2\pi \right]$

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