Verified Solution • 2025–26 Session moderate

QJEEAdv23Mabba6: JEE Advanced 2023 Mathematics - Class 12 JEEAdv23Mabba6 Solution: Let , for . Then the number of real solutions of the equation…

Let tan⁡−1(x)∈(−π2,π2)\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) , for x∈Rx \in \mathbb{R} . Then the number of real solutions of the equation 1+cos⁡(2x)=2tan⁡−1(tan⁡x)\sqrt{1+\cos (2 x)}=\sqrt{2} \tan ^{-1}(\tan x) in the set (−3π2,−π2)∪(−π2,π2)∪(π2,3π2)\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 :

Step-by-Step Verified Solution

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

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JEE Advanced 2023 Paper 1 Online Mathematics - Inverse Trigonometric Functions Question 2 English Explanation

Number of solution =3=3 .

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