Well, you can expand 10cos(2t-α) to 10cos(2t)cos(α)+10sin(2t)sin(α), and then equate one of the terms. So for example, the coefficient of sin(2t) on both sides is 10sin(α)=8, so α=arcsin(4/5). You could also write this is α=arccos(3/5) or α=arctan(4/3), and if you want to see why you can draw a...