Given,2cos t =-sqrt 3 cost tan t-cost
rArr2cost=-sqrt3 cost. sint/cost-cost
rArr2cost+cost=-sqrt3 sint
rArr3cost=-sqrt3 sint [squring both sides]
rArr (3cost)^2=(-sqrt3 sint)^2
rArr9cos^2 t = 3 sin^2 t
rArr3cos^2 t =sin^2 t
rArr3(1-sin^2 t)= sin^2 t
rArr3-3sin^2 t= sin^2 t
rArr 4sin^2 t=3
rArr sin^2 t =3/4
rArr sin t=(sqrt 3)/(sqrt 4)
rArr sin t = (sqrt3)/2=sin60
rArr t=60