Q: The number of roots of the equation x + 2tanx = π/2 in the interval [0, 2π] is

(A) 1

(B) 2

(C) 3

(D) infinite

Sol. We have x + 2 tanx = π/2 or tan x = π/4 – x/2.

Now the graphs of the curve y = tanx and y = π/4- x/2, in the interval [0, 2π] intersect at three points.

The abscissa of these three points are the roots of the equation.

Hence (C) is the correct answer.