Expanding powers of cosine

*To*: mathgroup at smc.vnet.net*Subject*: [mg84184] Expanding powers of cosine*From*: michael.p.croucher at googlemail.com*Date*: Wed, 12 Dec 2007 20:02:45 -0500 (EST)

Hi I would like to express even powers of Cos[x] in terms of powers of Sin[x] using the identity Sin[x]^2+Cos[x]^2 = 1. For example Cos[x]^4 = 1 - 2 Sin[x]^2 + Sin[x]^4 I could not get any of Mathematica's built in functions to do this for me so I created my own rule: expandCosn[z_] := Module[{s, res}, s = Cos[x]^n_ :> (1 - Sin[x]^2) Cos[x]^(n - 2) ; res = z //. s; Expand[res] ] which works fine: In[14]:= expandCosn[Cos[x]^4] Out[14]= 1 - 2 Sin[x]^2 + Sin[x]^4 My question is - have I missed something? Is there an easier way to do this? Cheers, Mike

**Follow-Ups**:**Re: Expanding powers of cosine***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>