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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If x takes all permissible negative values, then sin - 1 ⁡ x is equal to

Options

  1. A- cos - 1 ⁡ 1 - x 2
  2. Bcos - 1 ⁡ x 2 - 1
  3. Cπ - cos - 1 ⁡ 1 - x 2
  4. Dcos - 1 ⁡ 1 - x 2

Correct answer

A. - cos - 1 ⁡ 1 - x 2

Step-by-step solution

Let x = - y , y > 0 ∴ sin - 1 ⁡ x = sin - 1 ⁡ - y = - sin - 1 ⁡ y = - cos - 1 ⁡ 1 - y 2 = - cos - 1 ⁡ 1 - x 2

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