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JEE Main201912 Apr 2019Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The value of sin - 1 ⁡ 12 13 - sin - 1 ⁡ 3 5 is equal to:

Options

  1. Aπ - cos - 1 ⁡ 33 65
  2. Bπ 2 - cos - 1 ⁡ 9 65
  3. Cπ - sin - 1 ⁡ 63 65
  4. Dπ 2 - sin - 1 ⁡ 56 65

Correct answer

D. π 2 - sin - 1 ⁡ 56 65

Step-by-step solution

sin - 1 ⁡ 12 13 - sin - 1 ⁡ 3 5 = tan - 1 ⁡ 12 5 - tan - 1 ⁡ 3 4   sin - 1 ⁡ x = tan - 1 ⁡ x 1 - x 2 = tan - 1 ⁡ 12 5 - 3 4 1 + 12 × 3 5 × 4 = tan - 1 ⁡ 33 56 = sin - 1 ⁡ 33 65 = cos - 1 ⁡ 56 65 = π 2 - sin - 1 ⁡ 56 65

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