Calculus
posted by Lisa .
Use a trig identity to combine two functions into one so you can solve for x. (The solution should be valid for any value of t).
3cos(t) + 3*sqrt(3)*sin(t)=6cos(tx)
I know that 6 cos(tx) can be 6(cos(t)cosx(x)+sin(t)sin(x))
I don't know where to go from there though.

what you have now is
3cost + 3√3 sint = 6cosx cost + 6sinx sint
for them to be identical, the coefficients must match:
3 = 6cosx
3√3 = 6sinx
looks like x = π/3