Hi, Recently in class, my professor went over a relationship that exists between trigonometric functions, T(x), and their complementary functions. That is: ∫ T(x)dx = W(x) + C ∫ coT(x)dx = -co[W(x)] + C Without really providing a proof, we were told this relationship. I've plugged in numbers and tried graphing the scenario and it works from what I've done so far. If anyone could provide me a formal proof through any source, that would be great since I need a bit more convincing. Also, is a limitation to this property that both W(x) and T(x) must be a combination trigonometric functions themselves? Since when trying to solve ∫cscxdx using the answer from ∫secdx, an answer cannot be found. Are there any other limitations? Also, regarding the identities: sinAcosB = 1/2 [sin(A-B) + sin(A+B) sinAsinB = 1/2 [cos(A-B) - cos(A+B)] cosAcosB = 1/2[cos(A-B) + cos(A+B)] Is there a formal proof readily accessible for these identities? Thanks!