AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cosh x=\frac{5}{4}\), then \(\tanh 3 x=\)
- A \(\frac{63}{65}\)
- B \(\frac{25}{26}\)
- C \(\frac{65}{67}\)
- D \(\frac{252}{265}\)
Answer & Solution
Correct Answer
(A) \(\frac{63}{65}\)
Step-by-step Solution
Detailed explanation
Given, \(\cosh x=\frac{5}{4}\) \(\Rightarrow e^x+e^{-x}=\frac{5}{2}\) Now, \(\left(e^x+e^{-x}\right)^3=e^{3 x}+e^{-3 x}+3 e^x e^{-x}\left(e^x+e^{-x}\right)\) \(\Rightarrow \frac{125}{8}=e^{3 x}+e^{-3 x}+\frac{15}{2} \Rightarrow e^{3 x}+e^{-3 x}=\frac{65}{8}\) and…
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