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  4. 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

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

Relations and Functions - Part 2

Solution:

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