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Trigonometric Equations

Solve: tan2x=tanx


tan2x=tanx

i.e. 2tanx1tan2x=tanx

i.e. 2tanx=tanxtan3x

i.e. tan3x+tanx=0

i.e. tanx(tan2x+1)=0

i.e. tanx=0 or 1+tan2x=0

But 1+tan2x=0 is not possible \tan^2 x \neq -1

Now, \tan x = 0 \implies x = n \pi, \;\;\; n \in Z