What is expand ((e^x-e^{-x})^2)/2 ?

The solution to expand ((e^x-e^{-x})^2)/2 is (e^{2x})/2-1+(e^{-2x})/2

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expand ((e^x-e^{-x})^2)/2

expand

\frac{( e ^{x} - e ^{- x} ) ^{2}}{2}

\frac{e ^{2 x}}{2} - 1 + \frac{e ^{- 2 x}}{2}

Solution steps

\frac{( e ^{x} - e ^{- x} ) ^{2}}{2}

(e^{x} - e^{- x})^{2} = e^{2 x} - 2 + e^{- 2 x}

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Apply rule

\frac{a}{a} = 1

\frac{2}{2} = 1

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

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(f (x) = 0.5 x^{2} - k (x) x - 8 k (x) (x)^{3} x - k (x)) k (x)

\frac{x + 3}{x ( x + 8 )}

(2 sin (x) - 1) (sin (x) + 1)

What is expand ((e^x-e^{-x})^2)/2 ?
The solution to expand ((e^x-e^{-x})^2)/2 is (e^{2x})/2-1+(e^{-2x})/2