# Sum to Product Trigonometric identity does not work

 P: 198 Hi, The identity $sin(u) + sin(v) = 2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2})$ http://en.wikipedia.org/wiki/List_of...uct_identities Does not always work. I put the equation : $(sin(u) + sin(v)) - (2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2}))$ With u equal to -4.1 and v equal to 99 into wolfram alpha and it gave me the answer -1.11022x10^-16 http://www.wolframalpha.com/input/?i...9%2F2%29%29%29 If the identity is true, shouldn't the answer always be 0? What's going on here? Thanks