How do you solve $tan 2 x - tan x = 0$ $Tan 2x - tan x=0$ ?

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Answer 1 · 2015-04-16T17:08:14

In this way:

$tan 2 x = tan x$ $tan2x=tanx$ and two tangents are equal if their argument are equal with the moltiplicity.

So:

$2 x = x + k π \Rightarrow x = k π$ $2x=x+kpirArrx=kpi$

acceptable because we have to remember that for the existence of the function tangent the argument has to be not $\frac{π}{2} + k π$ $pi/2+kpi$ ,

so:

$2 x \neq \frac{π}{2} + k π \Rightarrow x \neq \frac{π}{4} + k \frac{π}{2}$ $2x!=pi/2+kpirArrx!=pi/4+kpi/2$

and

$x \neq \frac{π}{2} + k π$ $x!=pi/2+kpi$ .

How do you solve Tan 2x - tan x=0tan2x−tanx=0Tan 2x - tan x=0?