Question 2.28: Express (a) 3e^x — 2e^-x in terms of cosh x and sinh x, (b)......
Express
(a) 3 \mathrm{e}^x-2 \mathrm{e}^{-x} in terms of cosh x and sinh x,
(b) 2 \sinh x+\cosh x \text { in terms of } \mathrm{e}^x \text { and } \mathrm{e}^{-x}.
Step-by-Step
\begin{aligned}(a)\quad & 3 \mathrm{e}^x-2 \mathrm{e}^{-x}=3(\cosh x+\sinh x)-2(\cosh x-\sinh x)=\cosh x+5 \sinh x \\(b)\quad& 2 \sinh x+\cosh x=\mathrm{e}^x-\mathrm{e}^{-x}+\frac{\mathrm{e}^x+\mathrm{e}^{-x}}{2}=\frac{3 \mathrm{e}^x-\mathrm{e}^{-x}}{2}\end{aligned}
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