hi

I'm trying to prove: tanx = x + (1/3)x^3 + (2/15)x^5 +...

using sinx = x - (1/3!)x^3 + (1/5!)x^5 -...

and cosx = 1 - (1/2!)x^2 + (1/4!)x^4 -...

my working is as follows:

tanx=sinx/cosx = (sinx)(cosx)^-1

I then take

(cosx)^-1 = [1 - (1/2!)x^2 + (1/4!)x^4 -...]^-1 ......(i)

and try using the binomial theorem

(1 + x)^-1 = 1 -x + x^2 - x^3 +... .......(ii)

but when i try to substitute (i) into (ii) i come unstuck!!

help please.