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KCET2007MathematicsInverse Trigonometric Functions

The solution of ⁻¹ x+2 ⁻¹ x= 2 3 is

Options

  1. A- 1 3
  2. B1 3
  3. C- 3
  4. D3

Correct answer

D. 3

Step-by-step solution

We have, ⁻¹ x+2 ⁻¹ x= 2 3 ⁻¹ x+2 ⁻¹ 1 x = 2 3 ⁻¹ x+ ⁻¹ ( 2 ( 1 x ) 1- ( 1 x )² )= 2 3 [ 2 ⁻¹ x= ⁻¹ 2 x 1-x² ] ⁻¹ x+ ⁻¹ ( 2 x x²-1 )= 2 3 ⁻¹ ( x+ 2 x x²-1 1- 2 x² x²-1 )= 2 3 x³-x+2 x x²-1-2 x² = ( 2 3 ) x³+x -1-x² = ( 2 3 ) x (x²+1 ) -1 (x²+1 ) =- 3 x= 3

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