Question

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

Answer 1

$4\cosh^3x-3\cosh x=4\left(\dfrac{e^x+e^{-x}}2\right)^3-3\dfrac{e^x+e^{-x}}2$
$=\dfrac{(e^x+e^{-x})^3-3(e^x+e^{-x})}2$
$=\dfrac{e^{3x}+3e^x+3e^{-x}+e^{-3x}-3e^x-3e^{-x}}2$
$=\dfrac{e^{3x}+e^{-3x}}2$
$=\cosh3x$