Zugdichte2r

2022-01-28

How do I simplify $\frac{\mathrm{sin}2x}{1-\mathrm{cos}2x}$?

cevarnamvu

Expert

We have
$\mathrm{cos}\left(2x\right)={\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x=2{\mathrm{cos}}^{2}\left(x\right)-1=1-2{\mathrm{sin}}^{2}x$
and then
$\frac{\mathrm{sin}\left(2x\right)}{1-\mathrm{cos}\left(2x\right)}=\frac{2\mathrm{sin}x\mathrm{cos}x}{1-1+2{\mathrm{sin}}^{2}x}=\mathrm{cot}x$

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