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JEE Main20254 Apr 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Considering the principal values of the inverse trigonometric functions, ⁻¹ ( 3 2 x+ 1 2 1-x^2 ),- 1 2 x 1 2 , is equal to

Options

  1. A4 + ⁻¹ x
  2. B6 + ⁻¹ x
  3. C-5 6 - ⁻¹ x
  4. D5 6 - ⁻¹ x

Correct answer

B. 6 + ⁻¹ x

Step-by-step solution

aligned & ⁻¹ ( 3 2 x+ 1 2 1-x^2 ), -1 2 x 1 2 & Let ⁻¹(x)= - 6 4 & x= , then & ⁻¹ ( 3 2 + 1 2 ) & ⁻¹ ( ( + 6 ) )= + 6 & ⁻¹(x)+ 6 aligned

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