if-cosh-u-iv-x-iy-show-that-x-2-cosh-2-u-y-2-sinh-2-u-1-and-x-2-cosh-2-v-y-2-sinh-2-v-1-where-sinhx-and-coshx-hhyperbolcfunction-

Tinku Tara June 4, 2023 Trigonometry 0 Comments

Question Number 25611 by nnnavendu last updated on 12/Dec/17

if cosh(u+iv)=x+iy , show that (x^2 /(cosh^2 u))+(y^2 /(sinh^2 u))=1 and (x^2 /(cosh^2 v))−(y^2 /(sinh^2 v))=1 where sinhx and coshx hhyperbolcfunction

$${if}\:{cosh}\left({u}+{iv}\right)={x}+{iy}\:,\:{show}\:{that} \\ $$$$\frac{{x}^{\mathrm{2}} }{{cosh}^{\mathrm{2}} {u}}+\frac{{y}^{\mathrm{2}} }{{sinh}^{\mathrm{2}} {u}}=\mathrm{1}\:\:{and}\:\:\frac{{x}^{\mathrm{2}} }{{cosh}^{\mathrm{2}} {v}}−\frac{{y}^{\mathrm{2}} }{{sinh}^{\mathrm{2}} {v}}=\mathrm{1} \\ $$$$ \\ $$$${where}\:\:\:\:{sinhx}\:{and}\:{coshx}\:\:\:\:{hhyperbolcfunction} \\ $$

Facebook Tweet Pin

if-cosh-u-iv-x-iy-show-that-x-2-cosh-2-u-y-2-sinh-2-u-1-and-x-2-cosh-2-v-y-2-sinh-2-v-1-where-sinhx-and-coshx-hhyperbolcfunction-

Leave a Reply Cancel reply