Applying the cosine addition and sine addition formulas proves the cofunction, add pi, and supplementary angle identities. Using the formulas, we see that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x); that sin(x + pi) = -sin(x), cos(x + pi) = -cos(x); and that sin(pi-x) = sin(x), cos( -x) = -cos(x). The formulas also give the tangent of a difference formula, for tan(alpha-beta).

I was wondering how I could prove this algebraically. I know I have to start off by converting -tanx to (-sinx/cosx), but I do not know where to go from there.