Question

Show how tan(x+45 degrees) = 6tanx can be written in the form 6tan^2 x-5x+1=0

Answer 1

tan(x + 45) = 6 tan x
\[\frac{ \tan x + \tan 45 }{ 1-\tan x.\tan45 }= 6 tan x\]
\[\frac{ \tan x + 1 }{ 1 - \tan x }=6 tan x\]
tan x + 1 = 6 tan x(1 - tan x)
tan x + 1 = 6 tan x - 6 tan^2 x
6 tan^2 x - 6 tan x + tan x + 1 = 0
6 tan^2 x - 5 tan x + 1 = 0

Answer 2

Thanks. :)