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Does $\sin^2(4x) + \cos^2 (4x)=1$? So even $\sin^2 (249023049x) + \cos^2 (249023049x) = 1$?

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Yes, it does. In fact, for every $x$ you have this identity $$ \cos(x)^2+\sin(x)^2=1 $$

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Got it. Thanks Gustavo! – Fomo Loco Apr 30 '13 at 21:57

Yes and yes (pretty quick, indeed).

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Yes indeed. Thank you again DonAntonio for the quick response! – Fomo Loco Apr 30 '13 at 21:57

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