Question

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Stiind ca sin^4 x-cos^4 x=1/5 calculati cos2x.

Answer 1

$\sin^4x-\cos^4x = \dfrac{1}{5}\\ \\ (\sin^2 x-\cos^2 x)(\sin^2 x+\cos^2 x) = \dfrac{1}{5}\\ \\ (\sin^2 x-\cos^2 x)\cdot 1 = \dfrac{1}{5}\Big|\cdot(-1) \\ \\ \cos^2 x - \sin^2 x = -\dfrac{1}{5}\\ \\ \cos(2x) = -\dfrac{1}{5}$