Question

Tan 45°. tan² 30° tan 60°
slove it​

Answer 1

`(√(3) )/(3) or (1)/(√(3) )`

Explanation:

We can break the problem into three parts,

tan45 = sin(45)/cos(45)=
`((√(2))/(2) )/((√(2))/(2) ) =1`

`tan^(2)30 =(tan30))^(2)=(sin30/cos30)^2=((1/2)/(√(3)/2))^2 =(1/√(3))^2`

`tan60=sin60/cos60=(√(3)/2 )/(1/2) =√(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