What is l(e^{-t}*e^tcos(t)) ?

The solution to l(e^{-t}*e^tcos(t)) is lcos(t)

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simplify l(e^{-t}*e^tcos(t))

simplify

l (e^{- t} \cdot e^{t} cos (t))

l cos (t)

Solution steps

l (e^{- t} e^{t} cos (t))

Apply exponent rule:

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

e^{- t} e^{t} = e^{- t + t}

= l e^{- t + t} cos (t)

Add similar elements:

- t + t = 0

= l e^{0} cos (t)

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 \cdot l cos (t)

Multiply:

1 \cdot cos (t) = cos (t)

= l cos (t)

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