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AP EAMCET2015MathematicsInverse Trigonometric Functions

If ⁻¹ (x- x^2 2 + x^3 4 - )+ ⁻¹ (x^2- x^4 2 + x^6 4 - )= 2 and 0 < x < 2 , then x is equal to

Options

  1. A1 2
  2. B1
  3. C-1 2
  4. D-1

Correct answer

B. 1

Step-by-step solution

Given that, ⁻¹ (x- x^2 2 + x^2 4 - ) ⁻¹ (x- x^4 2 + x^6 4 - )= 2 Here, x- x^2 2 + x^3 4 - Forms G.P. so its sum can be given as x 1- x 2 Similarly, for series x^2- x^4 2 + x^6 4 - sum = x^2 1- x^2 2 array ll ⁻¹ [ x 1- x 2 ]+ ⁻¹ [ x^2 1- x^2 2 ]= 2 & ⁻¹ [ 2 x 2-x ]+ ⁻¹ [ 2 x^2 2-x^2 ]= 2 & & [ ⁻¹ x+ ⁻¹ x= 2 ] array aligned & 2 x 2-x = 2 x^2 2-x^2 & 1 2-x = x 2-x^2 & (2-x^2 )=x(2-x) & 2-x^2=2 x-x^2 & 2 x=2 x=1 aligned

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