Q64 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

If $\operatorname{cosech} x=\frac{4}{5}$, then $\cosh x=$

  • A
    $\sqrt{\frac{41}{21}}$
  • B
    $\sqrt{\frac{41}{19}}$
  • C
    $\sqrt{\frac{41}{25}}$
  • Correct answer
    D
    $\sqrt{\frac{41}{16}}$

Solution

$\operatorname{cosec} h x=\frac{1}{\sin h x}=\frac{4}{5}$ $\sin h x=5 / 4$ $\cos h^2 x=1+\sin h^2 x$ $=1+\left(\frac{5}{4}\right)^2=\frac{41}{16}$ $\therefore \cos h x=\sqrt{\frac{41}{16}}$

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

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