Q69 / 160 · AP EAMCET 2006 · Mathematics

$e^{\log \left(\cos h^{-1} 2\right)}$ is equal to :

  • A
    $\log (2-\sqrt{3})$
  • B
    $\log (\sqrt{3}-2)$
  • Correct answer
    C
    $\log (2+\sqrt{3})$
  • D
    $\log (2+\sqrt{5})$

Solution

$e^{\log \left(\cosh ^{-1} 2\right)}$ $=\cosh ^{-1}(2)=\log \left(2+\sqrt{2^2-1}\right)$ $=\log (2+\sqrt{3})$

Hence, the correct answer is option: 'C'.

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