# Multiply and simplify: frac{(sin theta+cos theta)(sin theta+cos theta)-1}{sin theta cos theta}

Multiply and simplify: $\frac{\left(\mathrm{sin}\theta +\mathrm{cos}\theta \right)\left(\mathrm{sin}\theta +\mathrm{cos}\theta \right)-1}{\mathrm{sin}\theta \mathrm{cos}\theta }$
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Liyana Mansell
Use the square of a binomal:
$\left(a+b{\right)}^{2}=\left(a+b\right)\left(a+b\right)={a}^{2}+2ab+{b}^{2}$
$=\frac{\left({\mathrm{sin}}^{2}\theta +2\mathrm{sin}\mathrm{cos}\theta +{\mathrm{cos}}^{2}\theta \right)-1}{\mathrm{sin}\theta \mathrm{cos}\theta }$
$=\frac{\left(2\mathrm{sin}\theta \mathrm{cos}\theta +{\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta \right)-1}{\mathrm{sin}\theta \mathrm{cos}\theta }$
Use the Pythagorean identity: ${\mathrm{sin}}^{2}\theta +{\mathrm{cos}}^{2}\theta =1$
$=\frac{\left(2\mathrm{sin}\theta \mathrm{cos}\theta +1\right)-1}{\mathrm{sin}\theta \mathrm{cos}\theta }$
Simplify:
$\frac{2\mathrm{sin}\theta \mathrm{cos}\theta }{\mathrm{sin}\theta \mathrm{cos}\theta }=2$