Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) = [e^x + e^(-x)]/2
sinh(2x)
= [e^(2x) - e^(-2x)]/2
= [e^x - e^(-x)][e^x + e^(-x)]/2
= 2 [[e^x - e^(-x)]/2][[e^x + e^(-x)]/2]
= 2sinh(x)cosh(x)
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Verified answer
Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) = [e^x + e^(-x)]/2
sinh(2x)
= [e^(2x) - e^(-2x)]/2
= [e^x - e^(-x)][e^x + e^(-x)]/2
= 2 [[e^x - e^(-x)]/2][[e^x + e^(-x)]/2]
= 2sinh(x)cosh(x)