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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The range of the function y = 2 sin - 1 ⁡ x 2 + 1 2 + cos - 1 ⁡ x 2 - 1 2 is (where, · denotes the greatest integer function)

Options

  1. A0 , π
  2. Bπ , 3 π 2
  3. Cπ
  4. Dπ , 3 π 2

Correct answer

D. π , 3 π 2

Step-by-step solution

Let, x 2 - 1 2 = x 2 + 1 2 - 1 = α ∈ I ⇒ x 2 + 1 2 - 1 = α ∴ y = 2 sin - 1 ⁡ α + 1 + cos - 1 ⁡ α , α = - 1,0 At α = - 1 y = 2 sin - 1 ⁡ 0 + cos - 1 ⁡ - 1 = π At α = 0 y = 2 sin - 1 ⁡ 1 + cos - 1 ⁡ 0 = 3 π 2

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