Trig Class Question, Please Help If You Can

Question

Find x where 0 ≤ x ≤ pi/2.

5sqrt(3)/3 cos x= 1 + sqrt(3) cos x

Answer 1

Multiply both sides by √3 : 5 cos x = √3 + 3 cos x

So 2 cos x = √3 and cos x = √3 / 2.

The only x in the interval [0, π/2] that satisfies this is x = π/6.