Q64 / 160 · AP EAMCET 2023 (18 May Shift 1) · Mathematics

$\log (\cosh 3+\sinh 3)+\log (\cosh 3-\sinh 3)=$

  • A
    $1$
  • B
    $2$
  • C
    $3$
  • Correct answer
    D
    $0$

Solution

$\log (\cosh 3+\sin h 3)+\log (\cosh 3-\sinh 3)$ $\begin{aligned} & =\log \left(\frac{\mathrm{e}^3+\mathrm{e}^{-3}}{2}+\frac{\mathrm{e}^3 \mathrm{e}^{-3}}{2}\right)+\log \left(\frac{\mathrm{e}^3+\mathrm{e}^{-3}}{2}-\frac{\mathrm{e}^3-\mathrm{e}^{-3}}{2}\right) \\ & =\log \left(\mathrm{e}^3\right)+\log \left(\mathrm{e}^{-3}\right) \\ & =3-3=0\end{aligned}$

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

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