Solve the equation 2tan2α=2tanα given that −π≤α<π. Separate your answers with commas.

Answer 1

divide both sides by 2

2tan2x = 2tanx

to get

tan2x = tanx

so, 2x = x or x= 0

x=0 which is between pi and -pi

if you tried to use the double angle formula though, tan2x = 2tanx/(1-tan^2x) you might be led to believe the only solution is imaginary and impossible.

but also x=-pi works

tan(2 x -180) = tan-360 = tan 360 = tan0 =0

and tan(-180) = 0

so two answers

x = 0, -180, or 0, - pi

Answer 2

2 tan 2α = 2 tan α is not possible.