Question

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(t-x)

I know that 6 cos(t-x) can be 6(cos(t)cosx(x)+sin(t)sin(x))
I don't know where to go from there though.

Answer 1

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