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
$tantheta=1/sqrt3$

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

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

If tantheta+cottheta=4 ÷ √3tantheta+cottheta=4 ÷ √3 then what is the value of thetatheta given that 0≤theta≤2π0≤theta≤2π ?