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![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)](https://image.slidesharecdn.com/provethehyperbolicfunctionformulasinhx2x2sinhxcoshxsol-230702161852-40cda0bb/85/Prove-the-hyperbolic-function-formula-sinhx-2x-2sinhxcoshxSol-pdf-1-320.jpg)
![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)](https://image.slidesharecdn.com/provethehyperbolicfunctionformulasinhx2x2sinhxcoshxsol-230702161852-40cda0bb/75/Prove-the-hyperbolic-function-formula-sinhx-2x-2sinhxcoshxSol-pdf-1-2048.jpg)
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Prove the hyperbolic function formula sinhx(2x)=2sinhxcoshxSol.pdf
The document provides a proof for the hyperbolic function formula sinh(2x) = 2sinh(x)cosh(x) using the definitions of sinh(x) and cosh(x). It involves expanding the expression for sinh(2x) based on the product of sinh(x) and cosh(x). The derivation confirms the formula is valid.
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Prove the hyperbolic function formula sinhx(2x)=2sinhxcoshxSol.pdf
- 1. Prove the hyperbolicfunction 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)