Number of real root s of equation x2 tan x=1 between -(3 π/2) and (3 π/2) is

Question

Number of real root s of equation x2 tan x=1 between -(3 π/2) and (3 π/2) is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

We have, x2 tan x=1 ⇒ x2=(1/ tan x) ⇒ x2= cot x Graph of y= cot x and y=x2 is shown below. <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-lwqmuwxr8ciyaaf6.jpg" /> Both graph intersects at 3 points in [- (3 π /2) , (3 π /2)] . Hence, no. of solutions are three.

Q. Number of real root $s$ of equation $x^{2}$ tan $x = 1$ between $- \frac{3 π}{2}$ and $\frac{3 π}{2}$ is

$1$

$2$

$3$

$4$

We have,
$x^{2} tan x = 1$
$\Rightarrow x^{2} = \frac{1}{t a n x}$
$\Rightarrow x^{2} = cot x$
Graph of $y = cot x$ and $y = x^{2}$ is shown below.

Both graph intersects at $3$ points in $[- \frac{3 π}{2}, \frac{3 π}{2}]$ . Hence, no. of solutions are three.

Q. Number of real root s of equation x2 tan x=1 between −23π​ and 23π​ is

1

2

3

4

We have, x2tanx=1 ⇒x2=tanx1​ ⇒x2=cotx Graph of y=cotx and y=x2 is shown below. Both graph intersects at 3 points in [−23π​,23π​] . Hence, no. of solutions are three.

Q. Number of real root $s$ of equation $x^{2}$ tan $x = 1$ between $- \frac{3 π}{2}$ and $\frac{3 π}{2}$ is

$1$

$2$

$3$

$4$

We have,
$x^{2} tan x = 1$
$\Rightarrow x^{2} = \frac{1}{t a n x}$
$\Rightarrow x^{2} = cot x$
Graph of $y = cot x$ and $y = x^{2}$ is shown below.

Both graph intersects at $3$ points in $[- \frac{3 π}{2}, \frac{3 π}{2}]$ . Hence, no. of solutions are three.