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MHT CET202526 Apr 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If y= ⁻¹ ( 1+ x 1- x ), 0 x < 2 , then y^ ( 6 )=

Options

  1. A- 1 4
  2. B1 6
  3. C1 4
  4. D1 2

Correct answer

D. 1 2

Step-by-step solution

Simplify the expression y = ⁻¹ 1+ x 1- x using half-angle identities. Observe that 1+ x 1- x = 1+ ( 2 -x ) 1- ( 2 -x ) = 2 ^2 ( 4 - x 2 ) 2 ^2 ( 4 - x 2 ) = ^2 ( 4 - x 2 ). Since 0 x ^2 ( 4 - x 2 ) = ( 4 - x 2 ). Apply the identity = ( 2 - ) to obtain y = ⁻¹ [ ( 2 - ( 4 - x 2 ) ) ] = ⁻¹ [ ( 4 + x 2 ) ]. For 0 x y = 4 + x 2 . Differentiate to find y' = 1 2 . Evaluate at x = 6 : y' ( 6 ) = 1 2 . 1 2

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