recall, cot(x) = 1/tan(x)

also note that . you only need to use one of these alternate forms.

now, draw a right triangle with an acute angle x, since cot(x) = adjacent/hypotenuse, you know the sides opposite and adjacent to this angle. use Pythagoras' theorem to find the other side. then you can find sin(x) and cos(x) and hence cos(2x). note you are in the fourth quadrant, so sine is negative, which cosine is positive. this doesn't really matter though, since we are squaring...