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AP EAMCET201920 Apr 2019Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The sum of the values of x satisfying the equation ⁻¹ ( 3 x 5 )+ ⁻¹ ( 4 x 5 )= ⁻¹(x) , is

Options

  1. A0
  2. B1 2
  3. C1 3
  4. D1 4

Correct answer

A. 0

Step-by-step solution

Given, equation aligned & ⁻¹ ( 3 x 5 )+ ⁻¹ 4 x 5 = ⁻¹ x, x [-1,1] & ⁻¹ ( 3 x 5 1- 16 x^2 25 + 4 x 5 1- 9 x^2 25 )= ⁻¹ x & 3 x 5 1- 16 x^2 25 + 4 x 5 1- 9 x^2 25 =x aligned Either x=0 aligned & or 3 25-16 x^2 25 + 4 25-9 x^2 25 =1 & 9 (25-16 x^2 )+16 (25-9 x^2 )+24 25-16 x^2 aligned aligned & 25-9 x^2 =625 & 24 25-16 x^2 25-9 x^2 =288 x^2 & (25-16 x^2 ) (25-9 x^2 )=144 x^4 & 625-625 x^2=0 x= 1 aligned So, sum of the values of ' x ' =0+1-1=0 Hence, option (a) is correct.

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