Question

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

• A. $5$
• B. $2$
• C. $4$
• D. $3$

Answer 1

The correct option is D $3$

$x+2\tan x=\frac{\pi }{2}$ in $[0,2\pi ]$
$2\tan x=\frac{\pi }{2}-x$
$\tan x=\frac{\pi }{4}-\frac{x}{2}$
$y=\tan x$ and $y=\frac{-x}{2}+\frac{\pi }{4}$


From the above graph it can be observed that there are $3$ intersection points in $[0,2\pi ]$
$\therefore$ Number of solutions $=3$