Mathematics: Prove that cosh3x = 4cosh^3(x)-3coshx

Prove that cosh3x = 4cosh^3(x)-3coshx - id34333525526, dannisundrop

Ответ:

ltawiah8393

08.01.2022

$4\cosh^3x-3\cosh x=4\left(\dfrac{e^x+e^{-x}}2\right)^3-3\dfrac{e^x+e^{-x}}2$
$=\dfrac{(e^x+e^{-x})^3-3(e^x+e^{-x})}2$
$=\dfrac{e^{3x}+3e^x+3e^{-x}+e^{-3x}-3e^x-3e^{-x}}2$
$=\dfrac{e^{3x}+e^{-3x}}2$
$=\cosh3x$

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Ответ:

bullockarwen

22.11.2022

Mathematics

i believe it is true,because the remainder would be 0

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