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Are you trying to write it in first degree terms of sine and cosine? If so, expand isn't the command to do this and I don't know off the top of my head if there is one that would do such a thing.How can I tell Mathematica to expand cos^5 t?
The command expand doesn't do it.
I learned something new today; I didn't realize that this was an option in Mathematica. The command:Is
$$\cos^{5}(t)=\frac{10\cos(t)+5\cos(3t)+\cos(5t)}{16}$$
helpful?
TrigReduce[Cos[x]^5]