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MHT CET202416 May 2024Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ⁻¹ ( x+1 x-1 )+ ⁻¹ ( x-1 x )= ⁻¹(-7) , then x is equal to

Options

  1. A-1
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

aligned & ⁻¹ ( x+1 x-1 )+ ⁻¹ ( x-1 x )= ⁻¹(-7) & ⁻¹ [ x+1 x-1 + x-1 x 1- ( x+1 x-1 ) ( x-1 x ) ]= ⁻¹(-7) aligned aligned & ⁻¹ [ x(x+1)+(x-1)(x-1) x(x-1)-(x+1)(x-1) ]= ⁻¹(-7) & ⁻¹ ( x^2+x+x^2-2 x+1 x^2-x-x^2+1 )= ⁻¹(-7) & ⁻¹ ( 2 x^2-x+1 1-x )= ⁻¹(-7) aligned aligned & 2 x^2-x+1 1-x =-7 & 2 x^2-8 x+8=0 & x^2-4 x+4=0 & (x-2)^2=0 & x=2 aligned

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