ExamBro
ExamBro
AP EAMCET · Maths · Hyperbola

If \(5 \sinh x-\cosh x=5\), then one of the values of \(\tanh x\) is

  1. A \(\frac{2}{5}\)
  2. B \(\frac{3}{5}\)
  3. C \(\frac{-3}{5}\)
  4. D \(\frac{-1}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{-3}{5}\)

Step-by-step Solution

Detailed explanation

\(5 \sinh x-\cosh x=5 \Rightarrow 5 \sinh x-5=\cosh x\) \(\Rightarrow 5(\sinh x-1)=\cosh x\) Squaring both sides \(25\left(\sinh ^2 x+1-2 \sinh x\right)=\cosh ^2 x\) \(\Rightarrow 24 \sinh ^2 x-50 \sinh x+24=0\) \(\Rightarrow(3 \sinh x-4)(4 \sin x-3)=0\)…