TS EAMCET · Maths · Functions
If \(x=\log _e 3\) then \(\tanh 2 x+\operatorname{sech} 2 x=\)
- A \(\frac{4}{3}\)
- B \(\frac{49}{41}\)
- C \(\frac{4}{5}\)
- D \(\frac{41}{49}\)
Answer & Solution
Correct Answer
(B) \(\frac{49}{41}\)
Step-by-step Solution
Detailed explanation
\( e^x = 3 \) \( e^{2x} = (e^x)^2 = 3^2 = 9 \) \( e^{-2x} = (e^{-x})^2 = (1/3)^2 = 1/9 \) \( \tanh 2x = \frac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}} = \frac{9 - 1/9}{9 + 1/9} = \frac{80/9}{82/9} = \frac{40}{41} \)…
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