Hi,
I'm having trouble solving the following for 0 > x > 2pi
tan x = 2 + tan 3x
i've used tan 3x = tan (x + 2x) = (tan x)(tan 2x) / 1 - (tan x)(tan 2x) a couple of times to get the equation in terms of tan x,
I.e.
3tan^3 - 4tan^2 - tan x + 2 = 0
which may or may not be correct.
but I'm not sure how to solve this polynomial.
Any help is much appreciated!
p.s. From Wolfram Alpha the solutions are pi*n - 3pi/4, pi*n - 5pi/8 and pi*n - pi/8
I'm having trouble solving the following for 0 > x > 2pi
tan x = 2 + tan 3x
i've used tan 3x = tan (x + 2x) = (tan x)(tan 2x) / 1 - (tan x)(tan 2x) a couple of times to get the equation in terms of tan x,
I.e.
3tan^3 - 4tan^2 - tan x + 2 = 0
which may or may not be correct.
but I'm not sure how to solve this polynomial.
Any help is much appreciated!
p.s. From Wolfram Alpha the solutions are pi*n - 3pi/4, pi*n - 5pi/8 and pi*n - pi/8