Question

Number of real solution of the equation $3x+\tan x=\frac{5\pi }{2}$ in $[0,\pi ]$, is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

$3x+\tan x=\frac{5\pi }{2}$

$\tan x=\frac{5\pi }{2}-3x$

Plot the graphs of,

$y=\tan x$

$y=\frac{5\pi }{2}-3x$

we get 2 points on: $0,\pi$

$0\Rightarrow (1.32,3.89)$

$\pi \Rightarrow (2.75,-0.408)$

2 points implies 2 solutions