# Tan^2(x)=tan(x)solve

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Both answers above are incomplete.

`tan^2x=tanx`

`tan^2x-tanx=0`

`tanx(tanx-1)=0`

`tanx=0` implies that `x=0+kpi` where k is an integer.(Or `k*180^@` if you are working in degrees)

`tanx=1` implies that `x=kpi + pi/4` where k is an integer. (Or `k*180^@+45^@`)

**Thus the full answer is `x=kpi",or,"x=kpi+pi/4` for `k in ZZ` .**

given tan^2x = tanx

thus tan^2x - tanx = 0 , (take tanx common)

tanx(tanx-1) = 0 , this shows that

either tanx =0 , or tanx-1 = 0

either x = tan^-1 (0) = pi/2, or tanx = 1

either x = pi/2 or x = tan^-1(1) = 45',

thus x= pi/2 or pi/4.

Q: find x , tan^2 x = tan x

A: tan^2 x = tan x

tan^2 x - tan x = 0

tan x( tan x - 1) = 0

So, either tan x = 0 or tan x -1 =0

either tan x = 0 or tan x = 1

but tan 0 = 0, tan 45 = 1

so **x= 0 or x= 45 (pi/4)**