prove that cosine is a continuous function!!
how do you prove that it is continuous using limit laws?
Prove that sin(x) and cos(x) are continuous at x= 0, first. Then use the fact that cos(x+y)= cos(x)cos(y)- sin(x)sin(y). How you prove that sin(x) and cos(x) are continuous at x= 0 depends on precisely how you have defined sine and cosine.