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Trigonometric constants

1) Express (cosx)^n in terms of sums of coskx
2) Express (sinx)^n in terms of sums of coskx or sinkx
3) Express cosnx in terms of sums of (cosx)^k
4) Express sinnx in terms of sums of (sinx)^k
5) Derive exact trigonometric identities for sin(k*pi) for k being:
1/12, 1/10,1/8,1/6,1/5,1/4,3/10,1/3,3/8,2/5,5/12

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This provides several examples of working with exact trigonometric constants.

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