How do you solve the following equation #tan 2x - tan x =0# in the interval [0, 2pi]?

Question

13062 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-18T00:40:49

This equation has no real roots.

Move #tan(x)# to the right:

#tan(2x) = tan(x)#

Substitute #(2tan(x))/(1 - tan^2(x)# for #tan(2x)#:

#(2tan(x))/(1 - tan^2(x)) = tan(x)#

Multiply by both sides by #(1 - tan^2(x))/tan(x)#

#2 = 1 - tan^2(x)#

#1 = - tan^2(x)#

#tan(x) = i#

This equation has no real roots.