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[itex]4(\sin^4x+\cos^4x) \equiv \cos4x + 3[/itex].

Really stuck with this, no idea how to go ahead with it. The book gives a hint: [itex]\sin ^4 x = (\sin ^2 x)^2[/itex] and use [itex]\cos 2x = 1 - 2\sin ^2 x[/itex]

But I don't even understand the hint, where did they get

[itex]\cos 2x = 1 - 2\sin ^2 x[/itex] from?