Prove the hyperbolic function formula: sinhx(2x)=2sinhxcoshx Solution Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) = [e^x + e^(-x)]/2 So, simply expand! 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).