Angle x is in the first quadrant and angle y is in the second quadrant, such that Cosx = 12/13 and Siny = 7/25. Determine an exact value for Cos(x+y).
If you draw the right triangles for x and y in standard position, you can see that
sinx = 5/13
cosy = -24/25
Now just use your sum formula
cos(x+y) = cosx cosy - sinx siny
= (12/13)(-24/25) - (5/13)(7/25) = -323/325