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


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

$i f c o s h (u + i v) = x + i y, s h o w t h a t$ $\frac{x^{2}}{{c o s h}^{2} u} + \frac{y^{2}}{{s i n h}^{2} u} = 1 a n d \frac{x^{2}}{{c o s h}^{2} v} - \frac{y^{2}}{{s i n h}^{2} v} = 1$ $w h e r e s i n h x a n d c o s h x h h y p e r b o l c f u n c t i o n$
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