Comprehension Passage

Direction : Consider the following for the items that follow :

Let f(x) = cos2x + x on [-π/2, π/2]. 

What is the greatest value of f(x)? 

1
\(\rm \frac{\sqrt3}{2}-\frac{\pi}{12}\)
2
\(\rm \frac{\sqrt3}{2}+\frac{\pi}{12}\)
3
\(\rm \frac{\sqrt3}{2}+\frac{\pi}{9}\)
4
\(\rm \frac{\sqrt3}{2}+\frac{\pi}{6}\)

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