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COMEDK202510 May 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

- 2 5 is the principal value of

Options

  1. A⁻¹ [ ( 7 5 ) ]
  2. B⁻¹ [ ( 7 5 ) ]
  3. C⁻¹ [ ( 7 5 ) ]
  4. D⁻¹ [ ( 7 5 ) ]

Correct answer

A. ⁻¹ [ ( 7 5 ) ]

Step-by-step solution

The principal value branch of ⁻¹(x) is [- /2, /2] . For ⁻¹( (7 /5)) , we write 7 /5 = + 2 /5 . Thus, (7 /5) = ( + 2 /5) = - (2 /5) = (-2 /5) . Since -2 /5 [- /2, /2] , the value is -2 /5 . The principal value branch of ⁻¹(x) is [0, ] /2 . For ⁻¹( (7 /5)) , we have 7 /5 = 2 - 3 /5 , so (7 /5) = (3 /5) . Since 3 /5 [0, ] , the value is 3 /5 . The principal value branch of ⁻¹(x) is (- /2, /2) . For ⁻¹( (7 /5)) , we have 7 /5 = + 2 /5 , so (7 /5) = (2 /5) . Since 2 /5 (- /2, /2) , the value is 2 /5 . The principal valu

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