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JEE Main20198 Apr 2019Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If α = c o s - 1 3 5 , β = t a n - 1 1 3 , where 0 < α , β < π 2 , then α - β is equal to

Options

  1. At a n - 1 9 14
  2. Bc o s - 1 9 5 10
  3. Csin - 1 ⁡ 9 5 10
  4. Dt a n - 1 9 5 10

Correct answer

C. sin - 1 ⁡ 9 5 10

Step-by-step solution

α = c o s - 1 3 5 = t a n - 1 4 3 ∴ a - β = t a n - 1 4 3 - t a n - 1 1 3 = t a n - 1 4 3 - 1 3 1 + 4 3 × 1 3 = t a n - 1 1 13 9 = t a n - 1 9 13 = sin - 1 ⁡ 9 5 10

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