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JEE Main20198 Apr 2019Morning ShiftMathematicsDifferentiationActual

If 2 y = cot - 1 3 cos x + sin x cos x - 3 sin x 2 ∀ x ∈ 0 , π 2 , then d y d x is equal to

Options

  1. Aπ 6 - x
  2. B2 x - π 3
  3. Cx - π 6
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

2 y = cot - 1 3 cos x + sin x cos x - 3 sin x 2 = cot - 1 3 + tan x 1 - 3 tan x 2 = cot - 1 tan π 3 + x 2 = cot - 1 cot π 2 - π 3 + x   2 ⇒ 2 y = π 6 - x 2 ,   x ∈ 0 , π 6 π + π 6 - x 2 ,   x ∈ π 6 , π 2 ⇒   2 d y d x = 2 π 6 - x . - 1 ⇒ d y d x = x - π 6 ,   x ∈ 0 , π 6 And d y d x = x - 7 π 6 ,   x ∈ π 6 , π 2 Left Hand and Right Hand Derivatives are not same so functi

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