AP EAMCET · Maths · Complex Number
For any real number \(n \in R,(\cosh x+\sinh x)^n=\)
- A \(\cosh n x-\sinh \mathrm{nx}\)
- B \(\cosh n x+\sinh \mathrm{nx}\)
- C \(\cosh ^2 n x+2 \sinh \mathrm{nx}\)
- D \(\cosh n x-\sinh \mathrm{nx}\)
Answer & Solution
Correct Answer
(B) \(\cosh n x+\sinh \mathrm{nx}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given }(\cosh x+\sinh x)^n \\ & (\cosh x+\sinh x)^n=\left(\frac{e^{i x}+e^{-i x}+e^{i x}-e^{-i x}}{2}\right)^n \\ & =\left(\frac{2 e^{i x}}{2}\right)^n=e^{i n x} \cdot \\ & =\frac{e^{i n x}+e^{i n x}}{2}=\frac{e^{i n x}+e^{-i n x}}{2}+\frac{e^{i n…
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