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COMEDK2025MathematicsInverse Trigonometric FunctionsActual

Given ( ⁻¹ x )= ( ⁻¹ 3 4 ) , then the value of x is

Options

  1. A1 2
  2. B4 3
  3. C3 4
  4. D1

Correct answer

C. 3 4

Step-by-step solution

Let = ⁻¹ x . Then = x . Since = 1 1 + ^2 , we have ( ⁻¹ x) = 1 1 + x^2 . Let = ⁻¹ 3 4 . Then = 3 4 , which implies = 4 3 . Using the identity = 1 1 + ^2 , we have ( ⁻¹ 3 4 ) = 1 1 + (3/4)^2 = 1 1 + 9/16 = 1 25/16 = 4 5 . Equating the two expressions: 1 1 + x^2 = 4 5 . Squaring both sides: 1 1 + x^2 = 16 25 . Thus, 1 + x^2 = 25 16 , which gives x^2 = 25 16 - 1 = 9 16 . Taking the square root, x = 3 4 . Answer: 3 4

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