Q65 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics

If $\sin \mathrm{h} x=\frac{\sqrt{21}}{2}$ then $\cosh 2 x+\sinh 2 x=$

  • A
    $\frac{21}{2}$
  • B
    $\frac{25}{2}$
  • Correct answer
    C
    $\frac{23+5 \sqrt{21}}{2}$
  • D
    $\frac{32+5 \sqrt{23}}{2}$

Solution

$\begin{aligned} & \quad \sinh x=\frac{\sqrt{21}}{2}, \cosh x=\sqrt{1+\sin ^2 h x}=\frac{\sqrt{25}}{2}=\frac{5}{2} \\ & \sinh 2 x=2 \sinh x \cosh x=\frac{5 \sqrt{21}}{2} \\ & \cosh 2 x=\cosh ^2 x+\sinh ^2 x=\frac{23}{2} \\ & \therefore \sinh 2 x+\cosh 2 x=\frac{23+5 \sqrt{21}}{2}\end{aligned}$

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

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