The number of real roots of the equation x2 tan x=1, where x ∈[0,2 π]- (π/2), (3 π/2) is equal to

Question

The number of real roots of the equation x2 tan x=1, where x ∈[0,2 π]- (π/2), (3 π/2) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

Θ tan x=(1/x2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f7e2053649366bff69ed7e954b592615-.png" /> Clearly graph of y= tan x y=(1/x2) intersect at two distinct points.

Q. The number of real roots of the equation $x^{2} tan x = 1$ , where $x \in [0, 2 π] - {\frac{π}{2}, \frac{3 π}{2}}$ is equal to

1

2

3

4

$Θ tan x = \frac{1}{x ^{2}}$

Clearly graph of $y = tan x & y = \frac{1}{x ^{2}}$ intersect at two distinct points.

Q. The number of real roots of the equation x2tanx=1, where x∈[0,2π]−{2π​,23π​} is equal to

1

2

3

4

Θtanx=x21​ Clearly graph of y=tanx&y=x21​ intersect at two distinct points.

Q. The number of real roots of the equation $x^{2} tan x = 1$ , where $x \in [0, 2 π] - {\frac{π}{2}, \frac{3 π}{2}}$ is equal to

$Θ tan x = \frac{1}{x ^{2}}$

Clearly graph of $y = tan x & y = \frac{1}{x ^{2}}$ intersect at two distinct points.