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COMEDK2024Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Evaluate: ⁻¹ (- 3 3 )- ⁻¹ (- 2 2 )- cosec ⁻¹(-1)- ⁻¹(1)

Options

  1. A- 2 3
  2. B0
  3. C3
  4. D6

Correct answer

C. 3

Step-by-step solution

The given expression is E = ⁻¹ (- 3 3 ) - ⁻¹ (- 2 2 ) - cosec ⁻¹(-1) - ⁻¹(1) . Simplify the arguments: 3 3 = 3 and 2 2 = 2 . Evaluate each term individually: 1. ⁻¹(- 3 ) = - ⁻¹( 3 ) = - 6 = 5 6 . 2. ⁻¹(- 2 ) = - ⁻¹( 2 ) = - 4 = 3 4 . 3. cosec ⁻¹(-1) = - cosec ⁻¹(1) = - 2 . 4. ⁻¹(1) = 4 . Substitute these values into the expression E : E = 5 6 - 3 4 - (- 2 ) - 4 . Combine the terms: E = 5 6 - 3 4 + 2 - 4 = 5 6 - + 2 = 5 - 6 + 3 6 = 2 6 = 3 . Answer: 3

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