Question 1117821
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There is nothing easier.


<pre>
Since cot(x) = {{{1/2}}}, then tan(x) = 2.


Next,  {{{tan(x-pi/6)}}} = apply the formula for the tan of difference = 


= {{{(tan(x)-tan(pi/6))/(1 + tan(x)*tan(pi/6))}}} = now substitute tan(x) = 2,  {{{tan(pi/6)}}} = {{{sqrt(3)/3}}}  to get 


= {{{(2-sqrt(3)/3)/(1+2*(sqrt(3)/3))}}} = {{{(6-sqrt(3))/(3+2*sqrt(3))}}} = {{{(6-sqrt(3))/(3+2*sqrt(3))}}}.{{{(3-2*sqrt(3))/(3-2*sqrt(3))}}} = {{{(18 + 2*3 - 3*sqrt(3) - 12*sqrt(3))/(3^2-(2*sqrt(3))^2)}}} = {{{(24-15*sqrt(3))/(-3)}}} = {{{-8 + 5*sqrt(3)}}} = 0.66 (approximately).
</pre>

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The answer and the solution by &nbsp;@stanbon &nbsp;are incorrect.