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solve the equation

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1 Answer

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-tan2x)which in our case gives=tanx.  If a solution for tanx≠0 is possible it would be
where 2/(1-tan2x)=1 or where 1-tan2x=2 or where tan2x=-1.  No other real angle save x=0 solves the problem.