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Question Number 177812 by Spillover last updated on 09/Oct/22

Answered by JDamian last updated on 09/Oct/22

$$\cosh \left(\ln x\right)=\frac{e^{\ln x}+e^{-\ln x}}{2}=\frac{x+\frac{1}{x}}{2}=\frac{x^2+1}{2x}=A$$$$\sinh \left(\ln x\right)=\frac{e^{\ln x}-e^{-\ln x}}{2}=\frac{x-\frac{1}{x}}{2}=\frac{x^2-1}{2x}=B$$$$A-B=\frac{1}{x}A+B=x$$$$\sqrt{\frac{A-B}{A+B}}=\frac{1}{x}$$$$\frac{1}{e^{-3\ln x}}=x^3$$$$$$$$x^3\frac{1}{x}=x^2$$

Commented by Spillover last updated on 09/Oct/22

$$\mathrm{nice}\mathrm{solution}$$

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