Question

The number of roots of the equation $x+2\tan x=\frac{\pi }{2}$ in the interval $[0,2\pi ]$ is

• A. $1$
• B. $2$
• C. $3$
• D. Infinite

Answer 1

Answer: (C)

$3$

Given, $x+2\tan x=\frac{\pi }{2}$

This equation also can be written as:

$\tan x=\frac{\pi }{4}-\frac{x}{2}$

plot the graph b/w $y=\tan x\text{and}y=\frac{\pi }{4}-\frac{x}{2}$

straight line cuts $y=\tan x,3$ times in the interval $[0,2\pi ]$.

$\therefore$ no. of roots=$3$.