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sin^2000(x) + cos^2000(x) = 1

I'm not sure how to go about it... I tried starting with sin^2(x) + cos^2(x) = 1 and build up to 2000 but I didn't get very far.

Obviously any multiple of pi will be an answer since either sin^2000 or cos^2000 will be 1 and the other will be 0. Are there others as well?

thx

-Kirstin.