jiayangchang
jiayangchang
07-03-2017
Mathematics
contestada
Prove that cosh3x = 4cosh^3(x)-3coshx
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LammettHash
LammettHash
07-03-2017
[tex]4\cosh^3x-3\cosh x=4\left(\dfrac{e^x+e^{-x}}2\right)^3-3\dfrac{e^x+e^{-x}}2[/tex]
[tex]=\dfrac{(e^x+e^{-x})^3-3(e^x+e^{-x})}2[/tex]
[tex]=\dfrac{e^{3x}+3e^x+3e^{-x}+e^{-3x}-3e^x-3e^{-x}}2[/tex]
[tex]=\dfrac{e^{3x}+e^{-3x}}2[/tex]
[tex]=\cosh3x[/tex]
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