AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\alpha=\log _e(2+\sqrt{3})\), then \(\frac{\cosh \alpha}{1-\tanh \alpha}+\frac{\sinh \alpha}{1-\operatorname{coth} \alpha}=\)
- A \(4+2 \sqrt{3}\)
- B \(7+4 \sqrt{3}\)
- C \(\frac{\sqrt{3}+1}{2}\)
- D \(2+\sqrt{3}\)
Answer & Solution
Correct Answer
(D) \(2+\sqrt{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\frac{\cos h \alpha}{1-\tan h \alpha}+\frac{\sin h \alpha}{1-\cot h \alpha} \\ & \Rightarrow I=\frac{\cos h^2 \alpha}{(\cos h \alpha-\sin \alpha)}+\frac{\sin h^2 \alpha}{(\sin h \alpha-\cos h \alpha)} \\ & \Rightarrow I=\frac{\cos h^2…
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