Question Number 25611 by nnnavendu last updated on 12/Dec/17
$${if}\:{cosh}\left({u}+{iv}\right)={x}+{iy}\:,\:{show}\:{that} \\ $$$$\frac{{x}^{\mathrm{2}} }{{cosh}^{\mathrm{2}} {u}}+\frac{{y}^{\mathrm{2}} }{{sinh}^{\mathrm{2}} {u}}=\mathrm{1}\:\:{and}\:\:\frac{{x}^{\mathrm{2}} }{{cosh}^{\mathrm{2}} {v}}−\frac{{y}^{\mathrm{2}} }{{sinh}^{\mathrm{2}} {v}}=\mathrm{1} \\ $$$$ \\ $$$${where}\:\:\:\:{sinhx}\:{and}\:{coshx}\:\:\:\:{hhyperbolcfunction} \\ $$