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JEE Main20203 Sep 2020Morning ShiftMathematicsInverse Trigonometric FunctionsActual

2 π - sin - 1 4 5 + sin - 1 5 13 + sin - 1 16 65 is equal to :

Options

  1. Aπ 2
  2. B5 π 4
  3. C3 π 2
  4. D7 π 4

Correct answer

C. 3 π 2

Step-by-step solution

sin - 1 4 5 + sin - 1 5 13 + sin - 1 16 65 = tan - 1 4 3 + tan - 1 5 12 + tan - 1 16 63 = tan - 1 4 3 + 5 12 1 - 4 3 · 5 12 + tan - 1 16 63 = tan - 1 63 16 + tan - 1 16 63 = π 2 ∴ 2 π - π 2 = 3 π 2

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