Let tan^-1(x) ∈ (-π/2, π/2) for x ∈ R. Then the number of real solutions of the equation ​

Question

Let \(\tan^{-1}(x) \in \left(-\frac \pi 2, \frac \pi 2\right), \) for x ∈ R. Then the number of real solutions of the equation \(\sqrt{1 + \cos(2x)} = \sqrt 2 \tan^{-1}(\tan x)\) 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 ____.

Answer 1

Number of solutions = Number of intersection points = 3