(1 + Tana) / (1-tana) = 3 + 2 √ 2, find sin2a

(1 + Tana) / (1-tana) = 3 + 2 √ 2, find sin2a

(1+tana)/(1-tana)=-1+2/(1-tana)=3+√2
1/(1-tana)=2+√2
1-tana=(2-√2)/2
tana=√2/2
sina/cosa=√2/2
(sina)^2/(cosa)^2=1/2
(sina)^2/(cosa)^2+1=3/2
[(cosa)^2+(sina)^2]/(cosa)^2=3/2
1/(cosa)^2=3/2
(cosa)^2=2/3
cota=1/tana=√2
(cota)^2=(cosa/sina)^2=2
(cosa/sina)^2+1=3
[(cosa)^2+(sina)^2]/(sina)^2=3
1/(sina)^2=3
(sina)^2=1/3
So (sinacosa) ^ 2 = 2 / 3 * 1 / 3 = 2 / 9
Because Sina / cosa = √ 2 / 2 〉 0
So sinacosa > 0
So sinacosa = √ 2 / 3
Sin2a = 2sinacosa = 2 radical 2 / 3