Question

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

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

Answer 1

Answer: (C)

We have, $x+2\tan x=\frac{\pi }{2}$
$\Rightarrow \tan x=\frac{\pi }{4}-\frac{x}{2}$
Let $y=\tan x$ and $y=\frac{\pi }{4}-\frac{x}{2}$
The curves $y=\tan x$ and $y=\frac{\pi }{4}-\frac{x}{2}$ in interval $[0,2\pi ]$, intersect at three points. The abscissa of these three points are the roots of the equation.