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KCET2023MathematicsInverse Trigonometric Functions

The value of ⁻¹ [ 1- x + 1+ x 1- x - 1+ x ] , where x (0, 4 ) is

Options

  1. Ax 2 -
  2. B- x 3
  3. C- x 2
  4. Dx 2

Correct answer

C. - x 2

Step-by-step solution

Here, ⁻¹ [ 1- x + 1+ x 1- x - 1- x ] aligned & = ⁻¹ [ ( 1- x + 1+ x )^2 (1- x)-(1+ x) ] & = ⁻¹ ( 1- x+1+ x+2 1- ^2 x 1- x-1- x ) & ⁻¹ ( 2+2 ^2 x -2 x ) & ^1 ( 1+ x - x ) aligned gathered ⁻¹ ( 1+2 ^2 x 2 -1 -2 x 2 x 2 ) ^1 ( - x 2 x 2 ) ⁻¹ (- x 2 )= ⁻¹ ( ( - x 2 ) ) = - x 2 gathered

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