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

1 Answer
Jun 23, 2018

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^@