Let tan^-1(x) ∈ (-(π)/2, (π)/2 ), for x ∈ R. Then the number of real solutions of the equation √(1+cos(2x)) = √(2) tan^-1(tan x) in the set (-(3π)/2, -(π)/2 ) ∪ (-(π)/2, (π)/2 ) ∪ ((π)/2, (3π)/2 ) is equal to

Let tan^-1(x) ∈ (-(π)/2, (π)/2 ), for x ∈ R. Then the… — JEE Advanced 2023 Mathematics PYQ

JEE Advanced 2023 · Paper 1 · numerical answer

Let

\tan^{-1}(x) \in \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)

, for

x \in \mathbb{R}

. Then the number of real solutions of the equation

\sqrt{1+\cos(2x)} = \sqrt{2}\, \tan^{-1}(\tan x)

in the set

\left(-\dfrac{3\pi}{2}, -\dfrac{\pi}{2}\right) \cup \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right) \cup \left(\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right)

is equal to

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Answer: 3

[JEE Advanced 2023 · Paper 1]

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