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MHT CET202525 Apr 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The principal value of ⁻¹ [ 1 2 ( 9 10 - 9 10 ) ] is

Options

  1. A3 20
  2. B17 20
  3. C7 10
  4. D10

Correct answer

B. 17 20

Step-by-step solution

Let y = ⁻¹ [ 1 2 ( 9 10 - 9 10 ) ] . Since 1 2 = 4 = 4 , we can rewrite the expression as: y = ⁻¹ [ 4 9 10 - 4 9 10 ] Applying the identity A B - A B = (A+B) with A = 4 and B = 9 10 : y = ⁻¹ [ ( 4 + 9 10 ) ] Combining terms: 4 + 9 10 = 5 + 18 20 = 23 20 Thus, y = ⁻¹ ( 23 20 ) The principal value branch of ⁻¹ is [0, ] , but 23 20 > . Using (2 - ) = : 23 20 = (2 - 23 20 ) = 17 20 Since 0 17 20 , the principal value is: y = 17 20 Final answer: 17 20

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