AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\tanh (x)=\frac{1}{3}\), then \(\tanh (3 x)\) is
- A \(\frac{8}{9}\)
- B \(\frac{7}{9}\)
- C 1
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{9}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \tanh (x)=\frac{1}{3}, \tanh (3 x)=? \\ & \Rightarrow \quad \frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{1}{3} \Rightarrow 2 e^x=4 e^{-x} \Rightarrow\left(e^{2 x}=2\right) \\ & \text {and } \tanh (3 x)=\frac{e^{3 x}-e^{-3 x}}{e^{3 x}+e^{-3 x}}=\frac{\left(e^{2…
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