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NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

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. Dπ 3 - x

Correct answer

C. x - π 6

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 d y d x = x -

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