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JEE Main 2021
Inverse Trigonometric Functions
Inverse Trigonometric Functions
Easy

Question

Considering only the principal values of inverse functions, the set A = { x \ge 0: tan -1 (2x) + tan -1 (3x) = π4{\pi \over 4}}

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Solution

tan -1 (2x) + tan -1 (3x) = π\pi /4 5x16x2 \Rightarrow \,\,{{5x} \over {1 - 6{x^2}}} = 1 \Rightarrow 6x 2 + 5x - 1 = 0 x = -1 or x = 16{1 \over 6} x = 16{1 \over 6} \because x > 0

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