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-

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

i f c o s h (u + i v) = x + i y, s h o w t h a t

\frac{x^{2}}{{c o s h}^{2} u} + \frac{y^{2}}{{s i n h}^{2} u} = 1 a n d \frac{x^{2}}{{c o s h}^{2} v} - \frac{y^{2}}{{s i n h}^{2} v} = 1

w h e r e s i n h x a n d c o s h x h h y p e r b o l c f u n c t i o n