Solve `cos 2x=|sin x|, x in (-pi/2, pi)`.

Explanation

We have
We have `cos 2x gt |sin x|, x in (-pi/2, pi)`
Draw the graph of `y= cos 2x` and `y=|sin x|` as shown in the folllowing figure.

To find points of intersection of graphs,
Let `cos 2x=sin x`
`:. 2 sin^(2) x+sin x-1=0`
`rArr sin x=-1, 1/2`
But `sin x ne -1`.
So, `sin x=1/2`
Clearly from the figure, graphs of `y=|sin x|` and `y=cos 2x` intersect at `x= pm pi/6, (5pi)/6`.
Therefore, the solutions set is `x in (- pi/6, pi/6) uu ((5pi)/6, pi)`.