# Find the Laplace transform of f(t) = (sin t – cos t)2

Find the Laplace transform of $f\left(t\right)=\left(\mathrm{sin}t–\mathrm{cos}t\right)2$
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averes8

Expand the square: ${\mathrm{sin}}^{2}\left(t\right)+{\mathrm{cos}}^{2}\left(t\right)-2\mathrm{sin}\left(t\right)\mathrm{cos}\left(t\right)=1-\mathrm{sin}\left(2t\right).$
Apply Laplace to each term: $F\left(s\right)=\frac{1}{s}-\frac{2}{{s}^{2}+4}$, because $L\left\{1\right\}=\frac{1}{s}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}L\left\{\mathrm{sin}\left(at\right)\right\}=\frac{a}{{s}^{2}+{a}^{2}}$.