NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The solution of the equation cos - 1 ⁡ x + cos - 1 ⁡ 2 x = 2 π 3 is

Options

Ax = 3 2 7
Bx = - 3 2 7
Cx = ± 1 2
DNone of these

Correct answer

A. x = 3 2 7

Step-by-step solution

cos - 1 ⁡ 2 x = 2 π 3 - cos - 1 ⁡ x … i Let, cos - 1 ⁡ 2 x = α ⇒ cos ⁡ α = 2 x cos - 1 ⁡ x = β ⇒ cos ⁡ β = x From i α = 2 π 3 - β cos ⁡ α = cos ⁡ 2 π 3 - β = cos ⁡ 2 π 3 cos ⁡ β + sin ⁡ 2 π 3 sin ⁡ β 2 x = - x 2 + 3 2 1 - x 2 25 x 2 4 = 3 4 1 - x 2 ⇒ 28 x 2 = 3 x = ± 3 2 7 But x = - 3 2 7 does not satisfy the given equation Hence, x = 3 2 7

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