# Identity 2 + 2cot^2x = 2cotx secx cscx

Kyran Hudson 2020-11-17 Answered
Identity $2+2{\mathrm{cot}}^{2}x=2\mathrm{cot}x\mathrm{sec}x\mathrm{csc}x$
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liannemdh
$2\mathrm{cot}\left(x\right)\mathrm{sec}\left(x\right)\mathrm{csc}\left(x\right)$
$=2\left(\frac{\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}\right)\left(\frac{1}{\mathrm{cos}\left(x\right)}\right)\left(\frac{1}{\mathrm{sin}\left(x\right)}\right)$
$=\frac{2\mathrm{cos}\left(x\right)}{\mathrm{cos}\left(x\right)\mathrm{sin}\left(x\right)\mathrm{sin}\left(x\right)}$
$=\frac{2}{\mathrm{sin}\left(x\right)\mathrm{sin}\left(x\right)}$
$=\frac{2}{{\mathrm{sin}}^{2}\left(x\right)}$
$=2{\mathrm{csc}}^{2}\left(x\right)$
$=2\left({\mathrm{csc}}^{2}\left(x\right)\right)$
$=2\left(1+{\mathrm{cot}}^{2}\left(x\right)\right)$
$=2+2{\mathrm{cot}}^{2}\left(x\right)$