Question

Tan 45°. tan² 30° tan 60° slove it​

Answer 1

Answer:

$\frac{\sqrt{3} }{3} or \frac{1}{\sqrt{3} }$

Step-by-step explanation:

We can break the problem into three parts,

tan45 = sin(45)/cos(45)=$\frac{\frac{\sqrt{2}}{2} }{\frac{\sqrt{2}}{2} } =1$

$tan^{2}30 =(tan30))^{2}=(sin30/cos30)^2=((1/2)/(\sqrt{3}/2))^2 =(1/\sqrt{3})^2$

$tan60=sin60/cos60=\frac{\sqrt{3}/2 }{1/2} =\sqrt{3}$

Then, $tan45*tan^230*tan60=1*(1/sqrt(3))^2*sqrt(3)=1/sqrt(3)=sqrt(3)/3$

Therefore, the solution is sqrt(3)/3