Trigonometry: tan2x=(3/4) what are the values of tanx?

Question

Trigonometry: tan2x=(3/4) what are the values of tanx?

Answer 1

tan2x = (3/4)

tan [x + x] = [2 tan x] /[1 - tan^2 x] = 3/4

3 - 3 tan^2 x = 8 tan x

3 tan^2 x + 8 tan x - 3 = 0

tan x = p

3 p^2 + 8 p - 3 = 0

3 p^2 + 9p - p - 3 =0

3p(p + 3) - 1(p + 3) =0

(p+3) (3p -1) =0

p = tan x = - 3 >>>>>>>> x = tan^-1 [- 3]

p = 1/3 = tan x >>>>>>>>>>> x = tan^-1[1/3]

Answer 2

let u=2x

tanu=3/4

arctan 3/4=u

arctan3/4=2x

(1/2)arctan3/4=x

tanx=tan((1/2)arctan3/4)