# Find L{f(t)} by first using an appropriate trigonometric identity. L is the symbol for Laplace transformation. f(t)=sin(2t)cos(2t) Laplace transform equation: L{f(t)}=int_0^infty e^(-st)f(t)dt

Find L{f(t)} by first using an appropriate trigonometric identity. L is the symbol for Laplace transformation.
$f\left(t\right)=\mathrm{sin}\left(2t\right)\mathrm{cos}\left(2t\right)$
Laplace transform equation: $L\left\{f\left(t\right)\right\}={\int }_{0}^{\mathrm{\infty }}{e}^{-st}f\left(t\right)dt$
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Rihanna Robles
A good trick here is to use a trig identity to separate your f(t) into a simple form.
$\mathrm{sin}\left(2t\right)+\mathrm{cos}\left(2t\right)=1/2\mathrm{sin}\left(2t+2t\right)+1/2\mathrm{sin}\left(2t-2t\right)=1/2\mathrm{sin}\left(4t\right)$
Now, you can plug this into your integral. To double check your answer you can use the table of laplace transforms, you canfind this anywhere on the internet, just google it. and from there you can easy convert things into laplace domain, provided you have them in the correct form.
so $L1/2sin\left(4t\right)=1/2\ast 4/\left({s}^{2}+{4}^{2}\right)$