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How do you find all values of x in the interval [0, 2pi] in the equation #tan 2x - tan x =0#?

1 Answer

Jan 31, 2016

#x = 0, pi, and 2pi#

Explanation:

Call tan x = t and apply the trig identity: #tan 2x = 2t/(1 - t^2)#
We get:
#(2t)/(1 - t^2) - t = (2t - t + t^3)/(1 - t^2) = 0#

#t + t^3 = 0 = t(1 + t^2) = 0.#
(1 + t^2) is always positive. There is one solution:
#t = tan x = 0# --> # x = 0, x = pi, and x = 2pi.#

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