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QJEEM21Ma4660: JEE Main 2021 Mathematics - Class 11 JEEM21Ma4660 Solution: The number of solutions of the equation x + 2tanx = in the…

The number of solutions of the equation x + 2tanx =

{\pi \over 2}

in the interval [0, 2

\pi

] is :

Step-by-Step Verified Solution

x + 2\tan x = {\pi \over 2}

in [0, 2

\pi

]

2\tan x = {\pi \over 2} - x

2\tan x = {\pi \over 2} - x

\tan x = {\pi \over 4} - {x \over 2}

y = \tan x

and

y = {{ - x} \over 2} + {\pi \over 4}

3 intersection points on the graph.

\therefore

3 solutions.