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JEE Main 2024 Mathematics question

MathematicsInverse Trigonometric FunctionsJEE Main 2024

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying tan⁻¹(x) + tan⁻¹(2x) = π/4 is :

Answer: (B)

Solution

Let f(x) = tan⁻¹x + tan⁻¹2x. Then f′(x) = 1/(1 + x²) + 2/(1 + 4x²) > 0, so f is strictly increasing with f(0) =

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Question ID VK-016639