Prove the addition formula for tangent.

The addition formula for tangent is tan(x+y) = (tanx + tany)/(1-tanx*tany).

To prove the addition formula for tangent, we start with the identity:

sin(x+y) = sinxcosy + cosxsiny

cos(x+y) = cosxcosy - sinxsiny

Dividing sin(x+y) by cos(x+y), we get:

tan(x+y) = (sinxcosy + cosxsiny)/(cosxcosy - sinxsiny)

Using the identities sin2x + cos2x = 1 and tanx = sinx/cosx, we can simplify the expression:

tan(x+y) = (tanx + tany)/(1-tanx*tany)

Therefore, the addition formula for tangent is proven.