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MHT CET202522 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Considering only the principal values of the inverse trigonometric function, the value of ( ⁻¹ 1 5 2 - ⁻¹ 4 17 ) is

Options

  1. A3 34
  2. B1 34
  3. C3 29
  4. D1 29

Correct answer

C. 3 29

Step-by-step solution

Given: Evaluate E = ( ⁻¹ 1 5 2 - ⁻¹ 4 17 ) . Let A = ⁻¹ 1 5 2 and B = ⁻¹ 4 17 , so E = (A - B) . Since A = 1 5 2 > 0 and A lies in [0, ] , we have A > 0 and can determine the opposite side: (5 2 )^2 - 1^2 = 7 . Thus, A = 7 . Similarly, B = 4 17 > 0 and B lies in [- 2 , 2 ] , so B > 0 and the adjacent side is ( 17 )^2 - 4^2 = 1 . Therefore, B = 4 . Apply the identity (A - B) = A - B 1 + A B . E = 7 - 4 1 + 7 4 = 3 29 The value is 3 29 , so the answer is C .

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