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JEE Main202628 January 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Considering the principal values of inverse trigonometric functions, the value of the expression (2 ⁻¹ ( 2 13 )-2 ⁻¹ ( 3 10 ) ) is equal to :

Options

  1. A16 63
  2. B- 33 56
  3. C- 16 63
  4. D33 56

Correct answer

D. 33 56

Step-by-step solution

Let = ⁻¹ ( 2 13 ) . Then = 2 13 , = 3 13 , = 2 3 . So (2 ) = 2 2 3 1 - 4 9 = 12 5 . Let = ⁻¹ ( 3 10 ) . Then = 3 10 , = 1 10 , = 1 3 . So (2 ) = 2 1 3 1 - 1 9 = 3 4 . Therefore (2 - 2 ) = 12 5 - 3 4 1 + 12 5 3 4 = 33 20 56 20 = 33 56

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