Answer 1

$\sin^4x-\cos^4x=0.5 \\ -(\cos^4x-\sin ^4x)=0.5 \\ (\cos^2x+\sin^2x)(\cos^2x-\sin^2x)=-0.5 \\ \cos2x=-0.5 \\ 2x=\pm \frac{2 \pi }{3} +2 \pi n, n \in Z \\ x=\pm \frac{ \pi }{3} + \pi n, n \in Z$

Answer 2

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