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#