What is expand ((e^x+e^{-x})^2)/4 ?

The solution to expand ((e^x+e^{-x})^2)/4 is (e^{2x})/4+1/2+(e^{-2x})/4

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expand ((e^x+e^{-x})^2)/4

expand

\frac{( e ^{x} + e ^{- x} ) ^{2}}{4}

\frac{e ^{2 x}}{4} + \frac{1}{2} + \frac{e ^{- 2 x}}{4}

Solution steps

\frac{( e ^{x} + e ^{- x} ) ^{2}}{4}

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

= \frac{e ^{2 x} + 2 + e ^{- 2 x}}{4}

Apply the fraction rule:

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

\frac{e ^{2 x} + 2 + e ^{- 2 x}}{4} = \frac{e ^{2 x}}{4} + \frac{2}{4} + \frac{e ^{- 2 x}}{4}

= \frac{e ^{2 x}}{4} + \frac{2}{4} + \frac{e ^{- 2 x}}{4}

Cancel

\frac{2}{4} : \frac{1}{2}

= \frac{e ^{2 x}}{4} + \frac{1}{2} + \frac{e ^{- 2 x}}{4}

\frac{8 x - 5}{( 4 x - 7 ) ^{2}}

x^{2} (10 - \frac{x ^{2}}{2})

(\frac{4}{2 - 5 x})^{3}

\frac{7 ( x + h ) ^{2}}{2}

(cos (a) + cos (b)) (cos (a) - cos (b))

What is expand ((e^x+e^{-x})^2)/4 ?
The solution to expand ((e^x+e^{-x})^2)/4 is (e^{2x})/4+1/2+(e^{-2x})/4