How do you solve $tan^2x+tanx=sqrt3 tanx + sqrt3$ for the domain $0<=x<=360$ ?

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Answer 1 · 2018-06-23T13:29:26

$tan^2x+tanx=sqrt3 tanx + sqrt3$

$=>tan^2x+tanx-sqrt3 tanx - sqrt3=0$

$=>tanx(tanx+1)-sqrt3( tanx +1)=0$

$=>(tanx+1)(tanx-sqrt3)=0$

When

#tanx+1=0

$=>tanx=-1=tan(180-45)=tan(360-45)$

So $x=135^@ or 315^@$

When

$tanx-sqrt3=0$

$=>tanx=sqrt3=tan60^@=tan(180+60)$

So $x=60^@ or 240^@$

How do you solve tan^2x+tanx=sqrt3 tanx + sqrt3tan^2x+tanx=sqrt3 tanx + sqrt3 for the domain 0<=x<=3600<=x<=360?