If #tantheta+cottheta=4 ÷ √3# then what is the value of #theta# given that #0≤theta≤2π# ?

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Answer 1 · 2018-01-23T16:44:31

#tantheta+ cottheta=4/sqrt3#

#=>tantheta+ 1/tantheta=4/sqrt3#

#=>sqrt3tan^2theta+ sqrt3=4tantheta#

#=>sqrt3tan^2theta-4tantheta+ sqrt3=0#

#=>sqrt3tan^2theta-3tantheta- tantheta+ sqrt3=0#

#=>sqrt3tantheta(tantheta-sqrt3)- (tantheta-sqrt3)=0#

#=>(tantheta-sqrt3)(sqrt3tantheta-1)=0#

When
#tantheta=sqrt3#

#=>tantheta=tan(pi/3)=tan(pi+pi/3)#

#theta=pi/3 or(4pi)/3#

When
#tantheta=1/sqrt3#

#=>tantheta=tan(pi/6)=tan(pi+pi/6)#

#theta=pi/6 or(7pi)/6#