If tan - 1 ⁡ 2 x + tan - 1 ⁡ 3 x = π 4 , then x =

Question

If tan - 1 ⁡ 2 x + tan - 1 ⁡ 3 x = π 4 , then x =, - 1, 1 3, 1 6, 1 2

MARKS App · Accepted Answer

tan − 1 2 x + tan − 1 3 x = π 4 tan − 1 ( 2 x + 3 x 1 − 6 x 2 ) = π 4 ; x > 0 5 x 1 − 6 x 2 = 1 5 x = 1 − 6 x 2 6 x 2 + 5 x − 1 = 0 6 x 2 + 6 x − x − 1 = 0 6 x ( x + 1 ) − 1 ( x + 1 ) = 0 ( 6 x − 1 ) ( x + 1 ) = 0 x ≠ − 1 ; x = 1 6

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