Question 249327
From here, use the unit circle:


<img src="http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png">



Recall that {{{tan(x)=sin(x)/cos(x)}}}. So {{{tan(45)=sin(45)/cos(45)=(sqrt(2)/2)/(sqrt(2)/2)=1}}} and {{{tan(30)=sin(30)/cos(30)=(1/2)/(sqrt(3)/2)=1/sqrt(3)}}}



In short, we have {{{tan(45)=1}}} and {{{tan(30)=1/sqrt(3)}}}



Simply plug these values into {{{(tan(45)+tan(30))/(1-tan(45)*tan(30))}}} to find {{{tan(45+30)}}}



Note: your answer should be {{{tan(75)=(sqrt(3)+1)/(sqrt(3)-1)}}}