Mathematics: Prove that sinh(x+y)=sinhxcoshy+sinhycoshx. i ve tried it from both side. one way i just get ((e^x)(-x)(e^-y))/2 and the other way i just get everything to cancel out and i get 1/ xd

Prove that sinh(x+y)=sinhxcoshy+sinhycoshx. i ve

Ответ:

Gearyjames8

05.01.2022

Hello,

$sh(x)= \dfrac{e^{x}-e^{-x}}{2}\\\\
ch(x)= \dfrac{e^{x}+e^{-x}}{2}\\\\

sh(x)ch(y)+ch(x)sh(y)= \dfrac{e^{x}-e^{-x}}{2}*\frac{e^{y}+e^{-y}}{2}+\frac{e^{x}+e^{-x}}{2}*\frac{e^{y}-e^{-y}}{2}\\\\



$
$= \dfrac{e^{x+y}-e^{-x+y}+e^{x-y}-e^{-(x+y)}+e^{x+y}+e^{-x+y}-e^{-(x+y)}}{4}\\\\


$
$=\dfrac{e^{x+y}-e^{-(x+y)}}{2}=sh(x+y)
$

0,0(0 оценок)

Ответ:

bigboyethanlanp2s9lm

22.08.2020

Mathematics

The answer would be (5,3)

0,0(0 оценок)

Prove that sinh(x+y)=sinhxcoshy+sinhycoshx. i've tried it from both side. one way i just get ((e^x)(-x)(e^-y))/2 and the other way i just get everything to cancel out and i get 1/ xd

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question