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

1 Answer
Mar 6, 2018

See the proof below

Explanation:

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