help with this question please.?

Question

tan(45 + x) = 2tan (45-x)

can anyone show me the working to this question. the answer is

tan^2 x - 6tanX+1 =0

Answer 1

tan(45 + x) = 2tan (45 - x)
tan (s + t) = (tan s + tan t) / (1 - tan s tan t)
tan (s - t) = (tan s - tan t) / (1 + tan s tan t)
(tan(45) + tan(x)) / (1 - tan(45)tan(x)) = 2(tan(45) - tan(x)) / (1 + tan(45)tan(x))
(1 + tan(x)) / (1 - tan(x)) = 2(1 - tan(x)) / (1 + tan(x))
(1 + tan(x))^2 = 2(1 - tan(x))^2
1 + 2tan(x) + tan^2(x) = 2 (1 - 2tan(x) + tan^2(x))
1 + 2tan(x) + tan^2(x) = 2 - 4tan(x) + 2tan^2(x)
tan^2(x) - 6tan(x) + 1 = 0
tan^2(x) - 6tan(x) + 9 - 9 + 1 = 0
(tan(x) - 3)^2 - 8 = 0
(tan(x) - 3 + 2√2)(tan(x) - 3 - 2√2) = 0
tan(x) = 3 - 2√2, 3 + 2√2
x = 9.7356°, 80.2644°

Answer 2

tan(45+x)=(1+tanx)/(1-tanx)=
2tan(45-x)=2(1-tanx)/(1+tanx)
so 1+2tanx+(tanx)^2=2-4tanx+2(tanx)^2
Then (tanx)^2-6tanx+1=0