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Trig Substitution

Re Mathematica 6.0.3 under WinXP.


Given a sum of (positive integer) powers of sin(t), I wish to cast (as much
as possible) the sum in terms of cos t, chiefly by substituting 1 - (cos
t)^2 for (sin t)^2 throughout.  The code below does this.




and[(1-Cos[t]^2)^Quotient[n,2] Sin[t]]};




What is an easier way?  Thankx.




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