Prove that Cosh(2x)=2cos2x-1?

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Answer 1 · 2018-03-06T10:35:57

See the proof below

I am going to prove the following

#cosh2x=2cosh^2x-1#

By the definition of hyperbolic functions

#cosh(2x)=(e^(2x)+e^(-2x))/2#

#coshx=(e^x+e^-x)/(2)#

#cosh^2x=((e^x+e^-x)/(2))^2#

#=1/4(e^x+e^-x)^2#

#=1/4(e^(2x)+e^(-2x)+2)#

Therefore,

#2cosh^2x-1=2*1/4(e^(2x)+e^(-2x)+2)-1#

#=(e^(2x)+e^(-2x))/2+1-1#

#=cosh(2x)#

#QED#