AP EAMCET · Maths · Trigonometric Equations
\(\cosh \alpha+\sinh \alpha=\mathrm{e}^3\) and \(\sinh \mathrm{x}=\frac{\alpha}{\alpha+1}\), then \(\tanh \mathrm{x}=\)
- A \(\frac{\alpha}{\alpha+2}\)
- B \(\frac{\alpha}{\alpha-3}\)
- C \(\frac{\alpha}{\alpha+4}\)
- D \(\frac{2 \alpha}{\alpha-1}\)
Answer & Solution
Correct Answer
(A) \(\frac{\alpha}{\alpha+2}\)
Step-by-step Solution
Detailed explanation
Since, \(\cos h \alpha+\sin h \alpha=e^3\) \(\Rightarrow \frac{e^\alpha+e^{-\alpha}}{2}+\frac{e^\alpha-e^{-\alpha}}{2}=e^3 \Rightarrow \alpha=3\) Now, \(\sin h x=\frac{\alpha}{\alpha+1}=\frac{3}{4}\)…
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