Find the number of solution to the equation `x^(2)tanx=1,x in [0,2pi].`

Explanation

We have `x^(2) tan x = 1`
`:." "tanx=(1)/(x^(2))`
Number of roots of the above equation =number of points (s) of intersection of the graphs of `y=tanx" and "y=(1)/(x^(2))" for "x in[0,2pi].`
Graphs of `y=tanx" and "y=(1)/(x^(2))` are shown in the following figure.

Graphs intersect at two points for `x in [0,2pi],` hence two roots.