Answer:
[tex]\frac{\sqrt{3} }{3} or \frac{1}{\sqrt{3} }[/tex]
Step-by-step explanation:
We can break the problem into three parts,
tan45 = sin(45)/cos(45)=[tex]\frac{\frac{\sqrt{2}}{2} }{\frac{\sqrt{2}}{2} } =1[/tex]
[tex]tan^{2}30 =(tan30))^{2}=(sin30/cos30)^2=((1/2)/(\sqrt{3}/2))^2 =(1/\sqrt{3})^2[/tex]
[tex]tan60=sin60/cos60=\frac{\sqrt{3}/2 }{1/2} =\sqrt{3}[/tex]
Then, [tex]tan45*tan^230*tan60=1*(1/sqrt(3))^2*sqrt(3)=1/sqrt(3)=sqrt(3)/3[/tex]
Therefore, the solution is sqrt(3)/3
