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JEE Main201912 Jan 2019Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Considering only the principal values of inverse functions, the set A = x ≥ 0 : tan - 1 2 x + tan - 1 3 x = π 4

Options

  1. AIs an empty set
  2. BContains more than two elements
  3. CContains two elements
  4. DIs a singleton

Correct answer

D. Is a singleton

Step-by-step solution

Given tan - 1 2 x + tan - 1 3 x = π 4 ⇒ t a n - 1 2 x + 3 x 1 - 2 x × 3 x = π 4 Applying tangent on both sides, ⇒ 5 x 1 - 6 x 2 = 1   ∵ tan π 4 = 1 ⇒ 5 x = 1 - 6 x 2 ⇒ 6 x 2 + 5 x - 1 = 0 ⇒ 6 x 2 + 6 x - x - 1 = 0 ⇒ 6 x - 1 x + 1 = 0 ⇒ x = - 1 ,   1 6 But, since x ≥ 0 . Hence, x = 1 6 ∴   A has only one element and thus, it is a singleton.

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