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AP EAMCET201921 Apr 2019Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If x ( - 2 , 2 ) , then x=

Options

  1. A2 cosech ⁻¹ ( ^2 x 2 -1 )
  2. B2 cosech ⁻¹ ( ^2 x 2 +1 )
  3. C2 coth ⁻¹ ( cosec ^2 x 2 -1 )
  4. D2 coth ⁻¹ ( cosec ^2 x 2 +1 )

Correct answer

C. 2 coth ⁻¹ ( cosec ^2 x 2 -1 )

Step-by-step solution

For aligned x & (- 2 , 2 ) & x=y( let ) aligned aligned & x=e^y x=e^ -y y = e^y-e^ -y e^y+e^ -y & y- y y+ y = e^ -y e^y = ^2 x & ( y 2 - y 2 y 2 + y 2 )^2= ^2 x & y 2 - y 2 y 2 + y 2 = x & 2 y 2 2 y 2 = 1+ x 1- x = ^2 x 2 aligned array rlrl & & coth y 1 & = ^2 x 2 = cosec ^2 x 2 -1 & y 2 & = coth ⁻¹ ( cosec ^2 x 2 -1 ) & y & =2 coth ⁻¹ ( cosec ^2 x 2 -1 ) array

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