2 tan x / 3 - tan^2 x = 1

Question

Stuck on this please help 

Answer 1

(2tanx)/3 - tan^2x = 1

2tanx -3tan^2(x) = 3

let y = tanx

2y - 3y^2 = 3

3y^2 -2y + 3 = 0

y = 2/6 + or - (1/6)sqr(4-36)= isqr32/6 = (2+or-isqr32)/6

tanx = two imaginary numbers, so odds are you intended the problem to read

2tan(x/3) - tan^2(x) = 1 Not (2tanx)/3 -tan^2(x) = 1

there is a third angle formula but it requires finding zeros of a cubic equation

tan3x = (3tanx - tan^3(x))/(1-3tan^2(x))

replace 3x by x and x by x/3,

but solving cubic equations is not easy