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

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

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

expand

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

e^{2 x} + 2 + e^{- 2 x}

Solution steps

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

Remove parentheses:

(a) = a

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = e^{x}, b = e^{- x}

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

Simplify

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

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

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tan (2 (x + \frac{π}{6}))

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