Q65 / 160 · AP EAMCET 2024 (18 May Shift 1) · Mathematics

$\cos h^{-1} 2=$

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

Solution

Since, we know, $\cosh ^{-1}(x)=\log \left(x+\sqrt{x^2-1}\right)$ $\Rightarrow \cos h^{-1}(2)=\log \left(2+\sqrt{2^2-1}\right)=\log (2+\sqrt{3})$

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

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