The total number of real solutions of the equation = ^ -1 (2 ) - 1 2 ^ -1 ( 6 9 + ^2 ) is (Here, the inverse trigonometric functions ^ -1 x and ^ -1 x assume values in [- 2 , 2 ] and (- 2 , 2 ), respectively.)

JEE Advanced 2025 Mathematics question

The total number of real solutions of the equation

θ = (2θ) - ()

is (Here, the inverse trigonometric functions and assume values in and , respectively.)

Answer: (C)

Let t = tan θ. , and of this equals when |t| ≤ 3 (and otherwise). The right side lies in , so θ does

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Question ID VK-035468