# Prove the identity: (sin x)/(1-cos x)=csc x+cot x

Prove the identity:
$\frac{\mathrm{sin}x}{1-\mathrm{cos}x}=\mathrm{csc}x+\mathrm{cot}x$
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treccinair
$\frac{\mathrm{sin}x}{1-\mathrm{cos}x}=\mathrm{csc}x+\mathrm{cot}x$
$\frac{\mathrm{sin}x}{1-\mathrm{cos}x}\ast \frac{\left(1+\mathrm{cos}x\right)}{\left(1+\mathrm{cos}x\right)}$

$=\frac{\mathrm{sin}x}{{\mathrm{sin}}^{2}x}+\frac{\mathrm{sin}x\mathrm{cos}x}{{\mathrm{sin}}^{2}x}$
$=\frac{1}{\mathrm{sin}x}+\frac{\mathrm{cos}x}{\mathrm{sin}x}$
$=\mathrm{csc}x-\mathrm{cot}x$
Jeffrey Jordon