Q67 / 160 · TS EAMCET 2024 (10 May Shift 2) · Mathematics

If $\sinh x=\frac{12}{5}$, then $\sinh 3 x+\cosh 3 x=$

  • Correct answer
    A
    125
  • B
    144
  • C
    169
  • D
    216

Solution

$\sinh x=\frac{12}{5}$ $\begin{aligned} & \frac{e^x-e^{-x}}{2}=\frac{12}{5} \Rightarrow e^x-\frac{1}{e^x}=\frac{24}{5} ; \text { Let } e^x=\mathrm{t} \\ & \Rightarrow t-\frac{1}{t}=\frac{24}{5} \Rightarrow 5 t^2-24 t-5=0 \\ & \Rightarrow t=-1,5 \\ & \Rightarrow t=5 \Rightarrow e^x=5 \Rightarrow e^{3 x}=125 \quad(t=-1 \text { not possible })\end{aligned}$ $\cos h 3 x+\sin h 3 x=e^{3 x}=125$

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

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