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JEE Main202226 Jun 2022Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If the inverse trigonometric functions take principal values, then cos - 1 3 10 cos tan - 1 4 3 + 2 5 sin tan - 1 4 3 is equal to

Options

  1. A0
  2. Bπ 4
  3. Cπ 3
  4. Dπ 6

Correct answer

C. π 3

Step-by-step solution

Let tan - 1 4 3 = θ ⇒ tan θ = 4 3 ∴ cos θ = 3 5   &   sin θ = 4 5 So, cos - 1 3 10 cos tan - 1 4 3 + 2 5 sin tan - 1 4 3 = cos - 1 3 10 cos θ + 2 5 sin θ = cos - 1 3 10 × 3 5 + 2 5 × 4 5 = cos - 1 9 50 + 8 25 = cos - 1 1 2 = π 3

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