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Inverse Trigonometric Functions question

2023 · Shift 1 · Q25

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PYQ Library
JEE Advanced
Mathematics
Inverse Trigonometric Functions
2023 · Shift 1 · Q25

Inverse Trigonometric Functions question

2023 · Shift 1 · Q25

JEE AdvancedMathematicsInverse Trigonometric FunctionsNumerical+4 / −1

Let

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

, for

x \in \mathbb{R}

. Then the number of real solutions of the equation

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

in the set

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

is equal to :

Numerical answer

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