tan (2x) -tan(x) = 0

tan(2x)=tan(x)

Clearly x=0 is a solution. Consider the formula tan(x+y)=(tanx+tany)/(1-tanxtany) for x=y gives

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

^{2}x)which in our case gives=tanx. If a solution for tanx≠0 is possible it would bewhere 2/(1-tan

^{2}x)=1 or where 1-tan^{2}x=2 or where tan^{2}x=-1. No other real angle save x=0 solves the problem.