What is e^{-st}((e^t+e^{-t})/2) ?

The solution to e^{-st}((e^t+e^{-t})/2) is (e^{-t-st}(e^{2t}+1))/2

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simplify e^{-st}((e^t+e^{-t})/2)

simplify

e^{- s t} (\frac{e ^{t} + e ^{- t}}{2})

\frac{e ^{- t - s t} ( e ^{2 t} + 1 )}{2}

Solution steps

e^{- s t} (\frac{e ^{t} + e ^{- t}}{2})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{s t}} \cdot \frac{e ^{t} + e ^{- t}}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot ( e ^{t} + e ^{- t} )}{e ^{s t} \cdot 2}

1 \cdot (e^{t} + e^{- t}) = e^{t} + e^{- t}

= \frac{e ^{t} + e ^{- t}}{2 e ^{s t}}

Factor

e^{t} + e^{- t} : e^{- t} (e^{2 t} + 1)

= \frac{e ^{- t} ( e ^{2 t} + 1 )}{e ^{s t} \cdot 2}

Cancel

\frac{e ^{- t} ( e ^{2 t} + 1 )}{e ^{s t} \cdot 2} : \frac{e ^{- t - s t} ( e ^{2 t} + 1 )}{2}

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

e^{- \frac{1}{9}}

\frac{( u r , v a l u e ) ^{- 3}}{160 \cdot 1 0 ^{- 6}}

cos (t) e^{t} \cdot (- 2) e^{t} sin (t)

e^{- 0.5 \cdot 4}

0.22 \cdot 1 0^{- 6}

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