Can you please prove sinh(2x)= 2 sinh(x) cos(x)?

1 Answer
James
May 12, 2018

#R.H.S=2 sinh(x) cosh(x)=2*[(e^x-e^-x)/2]*[(e^x+e^-x)/2]=#

#[(e^(2x)+1-1-e^(-2x))/2]=[e^(2x)-e^(-2x)]/2=sinh(2x)=L.H.S#

Explanation:

show below

#sinh(2x)=2 sinh(x) cosh(x)#

#R.H.S=2 sinh(x) cosh(x)=2*[(e^x-e^-x)/2]*[(e^x+e^-x)/2]=#

#[(e^(2x)+1-1-e^(-2x))/2]=[e^(2x)-e^(-2x)]/2=sinh(2x)=L.H.S#

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