# Quick question, does $\sin^2(4x) + \cos^2 (4x)$ equal 1?

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 $$\cos(x)^2+\sin(x)^2=1$$