The number of roots of the equation `xsinx=1,x in [-2pi,0)uu(0,2pi]` is (a) 2 (b) 3 (c) 4 (d) 0

Explanation

We have x sin x = 1
`therefore` `sin x = (1)/(x)`
Number of roots of the above equation = number of points (s) of the intersection of the graphs of `y = sin x` and `y = (1)/(x)` for `x in [-2pi, 0) uu (0, 2pi]`
The graphs of both functions are as shown in the following figure.

Graphs intersect at four points, hence four roots.