The "difference formula" for cosine is . Here, and . So . I don't know where you got " " but radians is 60 degrees. Draw an equilateral triangle with each side of length s and drop a perpendicular from one vertex to one side. That divides the triangle into two right triangles having hypotenuse of length s and one leg, the one at the 60 degree angle, of length (1/2)s. The cosine is "near side over hypotenuse", , NOT .