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AP EAMCET202120 Aug 2021Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If x = sin 2 tan - 1 2 , y = cos 2 tan - 1 3 , z = sec 3 tan - 1 4 then

Options

  1. Ax < y < z
  2. By < z < x
  3. Cz < x < y
  4. Dz < y < x

Correct answer

D. z < y < x

Step-by-step solution

We know, 2 tan - 1 x = sin - 1 ( 2 x 1 + x 2 )   = cos - 1 ( 1 - x 2 1 + x 2 ) = sec - 1 ( 1 + x 2 1 - x 2 ) ∴ x = sin 2 tan - 1 2     =   sin sin - 1 2 2 1 + 2 2   =   4 5 y = cos 2 tan - 1 3   =   cos cos - 1 ( 1 - 3 2 1 + 3 2 )   =   - 4 5 z = sec 2 tan - 1 4   sec sec - 1 ( 1 + 4 2 1 - 4 2 )   =   - 5 4 ∴ z < y < x

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