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MHT CET20192 May 2019Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The value of tan - 1 ⁡ 1 3 + tan - 1 ⁡ 1 5 + tan - 1 ⁡ 1 7 + tan - 1 ⁡ 1 8 is ________

Options

  1. A11 π 5
  2. Bπ 4
  3. Cπ
  4. D3 π 4

Correct answer

B. π 4

Step-by-step solution

Let L = t a n - 1 1 3 + t a n - 1 1 5 + t a n - 1 1 7 + t a n - 1 1 8 = t a n - 1 1 3 + 1 5 1 - 1 3 . 1 5 + t a n - 1 1 7 + 1 8 1 - 1 7 . 1 8 = t a n - 1 8 14 + t a n - 1 15 55 = t a n - 1 4 7 + t a n - 1 3 11 = t a n - 1 4 7 + 3 11 1 - 4 7 . 3 11 = t a n - 1 44 + 21 77 - 12 t a n - 1 65 65 = π 4

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