Using the following form of the cosine of a double angle formula, cos 2α = 1− 2sin2 α, we have:

`cos 2x=1-2 sin^2x`

`=1-2((-12)/13)^2`

`=1-2(144/169)`

`=(169-288)/169`

`=(-119)/169`

Notice that we didn't find the value of x using calculator first, and then find the required value. If we had done that, we would not have found the exact value, and we would have missed the pleasure of seeing the double angle formula in action :-)