Question

Prove that cosh3x = 4cosh^3(x)-3coshx

Answer 1

`4\cosh^3x-3\cosh x=4\left(\frac{e^x+e^(-x)}2\right)^3-3\frac{e^x+e^(-x)}2`

`=\frac{(e^x+e^(-x))^3-3(e^x+e^(-x))}2`

`=\frac{e^(3x)+3e^x+3e^(-x)+e^(-3x)-3e^x-3e^(-x)}2`

`=\frac{e^(3x)+e^(-3x)}2`

`=\cosh3x`