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

Question

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, π 6 - x, 2 x - π 3, x - π 6, π 3 - x

MARKS App · Accepted Answer

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 - 7 π 6 , x ∈ π 6 , π 2 x - π 6 is matching with one of the given options.

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