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AP EAMCET20225 Jul 2022Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Let x R and | x | < 1 . Then ⁻¹ x=

Options

  1. A1 2 ( 1+x 1-x )
  2. B1 2 ( 1-x 1+x )
  3. C1 2 (x+ 1-x^2 )
  4. D1 2 (x- 1-x^2 )

Correct answer

A. 1 2 ( 1+x 1-x )

Step-by-step solution

Let y= h⁻¹ x aligned & x= h y & x= e^y-e^ -y e^y+e^ -y aligned aligned & x e^y+e^ -y x=e^y-e^ -y & (1-x) e^y=(1+x) e^ -y & e^ 2 y =(1-x)=(1+x) aligned aligned & e^ 2 y = ( 1+x 1-x ) & e^ 2 y = ( 1+x 1-x ) aligned aligned & 2 y= ( 1+x 1-x ) & y= 1 2 ( 1+x 1-x ) aligned

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