Question

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

Answer 1

Answer: (C)

3

Answer 2

We have x + 2 tanx = π/2

or tan x = π/4 – x/2

Now the graphs of the curves 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