# Find the Laplace transform of \sin h t-\cos h t

Reggie 2021-09-03 Answered
Find the Laplace transform of $\mathrm{sin}ht-\mathrm{cos}ht$
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## Expert Answer

Velsenw
Answered 2021-09-04 Author has 91 answers
Step 1
Given
$y\left(t\right)=\mathrm{sin}h\left(t\right)-\mathrm{cos}h\left(t\right)$
Step 2
$y\left(t\right)=\mathrm{sin}h\left(t\right)-\mathrm{cos}h\left(t\right)$
$y\left(t\right)=\left[\frac{{e}^{t}-{e}^{-t}}{2}\right]-\left[\frac{{e}^{t}+{e}^{-t}}{2}\right]$
$y\left(t\right)=-\frac{2{e}^{-t}}{2}$
$y\left(t\right)=-{e}^{-t}$
Now laplace transform is
$L\left(y\left(t\right)\right)=-L\left({e}^{-t}\right)$
$y\left(s\right)=-\frac{1}{s+1}$
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