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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.

  • Calculus -

    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

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