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AP EAMCET201921 Apr 2019Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

e sec h - 1 1 2 + tan h - 1 1 2 + sin h - 1 1 2 =

Options

  1. A2 + 3 3 + 2 5 + 3 15 2
  2. B3 + 2 3 + 3 5 + 2 15 2
  3. C2 + 3 3 + 4 5 + 5 15 2
  4. D2 + 3 3 - 4 5 + 5 15 2

Correct answer

B. 3 + 2 3 + 3 5 + 2 15 2

Step-by-step solution

We know that, sec h - 1 x = log 1 + 1 - x 2 x tan h - 1 x = 1 2 log 1 + x 1 - x sin h - 1 x = log x + x 2 + 1 Substitute the values in the given equation and simplify. e log 1 + 1 - 1 4 1 2 · 1 2 log 1 + 1 2 1 - 1 2 + log 1 2 + 1 4 + 1 = 2 + 3 3 5 + 1 2 = 2 3 + 3 5 + 1 2 = 2 15 + 2 3 + 3 5 + 3 2 = 3 + 3 5 + 2 3 + 2 15 2

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