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COMEDK20269 May 2026Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0

Options

  1. A2 ⁻¹x
  2. B⁻¹x
  3. C1 2 ⁻¹x
  4. D⁻¹ x 2

Correct answer

C. 1 2 ⁻¹x

Step-by-step solution

Let x = , where (- /2, /2) and 0 . Substituting x = in the given expression: ⁻¹ ( 1+ ^2 - 1 ) = ⁻¹ ( - 1 ) = ⁻¹ ( 1 - 1 ) = ⁻¹ ( 1 - ) Using the trigonometric identities 1 - = 2 ^2( /2) and = 2 ( /2) ( /2) : = ⁻¹ ( 2 ^2( /2) 2 ( /2) ( /2) ) = ⁻¹ ( ( /2) ) Since (- /2, /2) , /2 (- /4, /4) , which lies in the principal value branch of ⁻¹ . = 2 Substituting back = ⁻¹x : = 1 2 ⁻¹x Answer: 1 2 ⁻¹x

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