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COMEDK20269 May 2026Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is:

Options

  1. A7 10
  2. B- 11 30
  3. C3 10
  4. D29 30

Correct answer

C. 3 10

Step-by-step solution

The principal value branch of ⁻¹x is [0, ] . ⁻¹ ( 7 6 ) = ⁻¹ ( (2 - 5 6 ) ) = ⁻¹ ( 5 6 ) = 5 6 The principal value branch of ⁻¹x is [- 2 , 2 ] . ⁻¹ ( 22 3 ) = ⁻¹ ( (7 + 3 ) ) = ⁻¹ (- 3 ) = - 3 The principal value branch of ⁻¹x is (- 2 , 2 ) . ⁻¹ ( 4 5 ) = ⁻¹ ( ( - 5 ) ) = ⁻¹ (- 5 ) = - 5 Adding the three values: 5 6 - 3 - 5 = 25 - 10 - 6 30 = 9 30 = 3 10 Answer: 3 10

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