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99 Percentile Qs Bank for JEE MainMathematicsInverse Trigonometric Functions

cos - 1 ⁡ 1 2 x 2 + 1 - x 2 1 - x 2 4 = cos - 1 ⁡ x 2 - cos - 1 ⁡ x holds for

Options

  1. A| x | ≤ 1
  2. Bx ∈ R
  3. C0 ≤ x ≤ 1
  4. D- 1 ≤ x ≤ 0

Correct answer

A. | x | ≤ 1

Step-by-step solution

It is given that cos - 1 x 2 2 + 1 - x 2 1 - x 2 4 = cos - 1 x 2 - cos - 1 x Since, 0 ≤ cos - 1 ⁡ x 2 2 + 1 - x 2 1 - x 2 4 ≤ π 2 Because cos - 1 ⁡ x is in first quadrant when x   is positive And cos - 1   ⁡ x 2 - cos - 1 ⁡ x ≥ 0 So, cos - 1   ⁡ x 2 ≥ cos - 1 ⁡ x Also, x 2 ≤ 1 ⇒ | x | ≤ 1

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