Homework Help

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

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t521863 | Student, Grade 10 | (Level 1) Valedictorian

Posted May 21, 2012 at 10:58 PM via web

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Tan^2(x)=tan(x)

solve

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 22, 2012 at 5:48 PM (Answer #1)

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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` .

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faiz3507 | High School Teacher | (Level 2) Adjunct Educator

Posted May 21, 2012 at 11:17 PM (Answer #2)

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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.

Top Answer

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lochana2500 | TA , Undergraduate | (Level 1) Valedictorian

Posted May 22, 2012 at 9:43 AM (Answer #3)

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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)

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