What is factor e^{ωt}+e^{-ωt} ?

The solution to factor e^{ωt}+e^{-ωt} is e^{-ωt}(e^{2ωt}+1)

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factor e^{ωt}+e^{-ωt}

factor

e^{ω t} + e^{- ω t}

e^{- ω t} (e^{2 ω t} + 1)

Solution steps

e^{ω t} + e^{- ω t}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{ω t} = e^{- ω t} e^{2 ω t}

= e^{- ω t} e^{2 ω t} + e^{- ω t}

Factor out common term

e^{- ω t}

= e^{- ω t} (e^{2 ω t} + 1)

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What is factor e^{ωt}+e^{-ωt} ?
The solution to factor e^{ωt}+e^{-ωt} is e^{-ωt}(e^{2ωt}+1)