# Finding cot &#x2061;<!-- ⁡ --> ( &#x03C0;<!-- π --> 12 </mfrac> ) Given:

Finding $\mathrm{cot}\left(\frac{\pi }{12}\right)$
Given:
$\mathrm{cot}\left(\theta -\varphi \right)=\frac{\mathrm{cot}\theta \mathrm{cot}\varphi +1}{\mathrm{cot}\theta -\mathrm{cot}\varphi }$
And:
$\mathrm{cot}\frac{\pi }{3}=\frac{1}{\sqrt{3}};\mathrm{cot}\frac{\pi }{4}=1$
$\frac{\frac{1}{\sqrt{3}}\left(1\right)+1}{\frac{1}{\sqrt{3}}-1}$
$\frac{1+\sqrt{3}}{1-\sqrt{3}}$
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Leslie Rollins
$\mathrm{cot}\left(\theta -\varphi \right)=\frac{\mathrm{cot}\left(\theta \right)\mathrm{cot}\left(\varphi \right)+1}{\mathrm{cot}\varphi -\mathrm{cot}\theta }$
Notice the denominator order. You switched them, hence switching the sign.
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Ayaan Barr
$\mathrm{cot}\frac{\pi }{12}=\frac{1+\mathrm{cos}\frac{\pi }{6}}{\mathrm{sin}\frac{\pi }{6}}=2+\sqrt{3}$