prove-that-cosh-2x-2cosh-2-x-1-

Question Number 17280 by tawa tawa last updated on 03/Jul/17

prove that : \cosh (2 x) = {2 \cosh}^{2} (x) - 1

Commented by mrW1 last updated on 03/Jul/17

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

= \frac{e^{2 x} + e^{- 2 x} + 2 - 2}{2}

= \frac{{(e^{x})}^{2} + 2 e^{x} e^{- x} + {(e^{- x})}^{2}}{2} - 1

= \frac{{(e^{x} + e^{- x})}^{2}}{2} - 1

= 2 {(\frac{e^{x} + e^{- x}}{2})}^{2} - 1

= 2 \cosh^{2} x - 1

Commented by tawa tawa last updated on 03/Jul/17

God bless you sir .