Homework SourseProve the hyperbolic function formula sinhx2x2sinhxcoshxSolu
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)![Prove the hyperbolic function formula: sinhx(2x)=2sinhxcoshxSolution Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) = [e^x](/WebImages/3/prove-the-hyperbolic-function-formula-sinhx2x2sinhxcoshxsolu-969220-1761499324-0.webp "Prove the hyperbolic function formula: sinhx(2x)=2sinhxcoshxSolution Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) = [e^x")
