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^@#