Solve the equation tanx+1/tanx=1+3tanx For 0<x<180?

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Answer 1 · 2017-11-13T19:26:21

#30^o#

#(tanx+1)/tanx=1+3tanx#

Multiply by #tanx#

#tanx+1=tanx+3tan^2x#

#-> tanx+1-tanx-3tan^2x=0#

#->cancel(tanx)+1cancel(-tanx)-3tan^2x=0#

#->1-3tan^2x=0#

#->tan^2x=1/3=>tanx=+-sqrt(1/3)=-1/sqrt(3) and 1/sqrt(3)#

#x=tan^-1(tanx)=tan^-1(1/sqrt(3))=pi/6=30^o#