Question

Find the number of real roots of the equation $x^2\tan x=1$ between $0\text{and}2\pi$

• A. 1
• B. 3
• C. 2
• D. 0

Answer 1

The correct option is C 2

Given equation is $x^2\tan x=1$
$\Rightarrow x^2=\frac{1}{\tan x}=\cot x$
Let $y=x^2=\cot x$

$\therefore y=x^2\text{and}y=\cot x$
Graphically, we observe that the number of solutions $=2$