Prove that:
(tan20°)^2+(tan40°^)2+(tan80°)^2=33

Step-by-step explanation:

We have tanπ3=−tan2π3=tan4π3=3–√

Since tan(3x)=3tanx−tan3x1−3tan2x

Thus tanπ/9,−tan2π/9,tan4π/9are solutions to the polynomial 3–√=3x−x31−3x2

On simplication, x3−33–√x2−3x+3–√=0.(1)

Since (tanπ9−tan2π9+tan4π9)2

=tan2π9+tan22π9+tan24π9

+ 2( -tanπ9tan2π9+tanπ8tan4π9−tan2π9tan4π9)

By sum and product pairs of roots in (1) above

(−33–√)2=tan2π9+tan22π9+tan24π9+2×−3

∴tan2π9+tan22π9+tan24π9=33

statement #3: proof- ang is congruent to ang ecd : angles are congruent.  

step-by-step explanation:

1: the missing angles in statement #3  

a.) acb  

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.  

2: the missing word in reason #3  

c.) vertical  

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.  

i hope that was and understanding.

it will take lin 15 minutes   to empty her hot tub