Q65 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

If $\frac{5 \sinh 2 x}{7+6 \cosh 2 x}=\frac{3}{2}$, then $3 \tan \mathrm{h}^2 x+20 \tan \mathrm{h} x=$

  • A
    13
  • B
    26
  • Correct answer
    C
    39
  • D
    $\frac{13}{2}$

Solution

$\begin{aligned} & \frac{5 \sinh 2 x}{7+6 \cosh 2 x}=\frac{3}{2} \\ & \Rightarrow \frac{10 \sinh x \cdot \operatorname{coshx}}{7+6\left(2 \cosh ^2 x-1\right)}=\frac{3}{2} \\ & \Rightarrow \frac{10 \sinh x \cdot \cosh x}{12 \cosh ^2 x+1}=\frac{3}{2} \\ & \Rightarrow \frac{10 \tanh x}{12+\operatorname{sech}^2 x}=\frac{3}{2} \\ & \Rightarrow \frac{10 \tanh x}{12+1-\tanh ^2 x}=\frac{3}{2} \\ & \Rightarrow \frac{10 \tan \mathrm{hx}}{13-\tan ^2 \mathrm{x}}=\frac{3}{2} \\ & \Rightarrow 20 \tan \mathrm{hx}=39-3 \tan ^2 \mathrm{x} \\ & \Rightarrow 3 \tan h^2 x+20 \tan h x=39 \\ & \end{aligned}$

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

Relevant Questions