Number of solutions of equation x +2 tan x =frac{π}{2} in interval [0,2 π] is :

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Trigonometrical Equations

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

A

$3$

B

$4$

C

$2$

D

$5$

(JEE MAIN-2021)

Solution

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

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

$\Rightarrow \tan x=-\frac{1}{2} x+\frac{\pi}{4}$

Number of soluitons of the given eauation is $'3'.$

Standard 11

Mathematics

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