Question

Question #6db48

Answer 1

`60^°`

Explanation:

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`