求值:(1-sin^6 x-cos^6 x)/(1-sin^4 x-cos^4 x)

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求值:(1-sin^6 x-cos^6 x)/(1-sin^4 x-cos^4 x)

因为sin^4 x+cos^4 x=(sin^2 x+cos^2 x)^2-2sin^2 x cos^2 x=1-2sin^2 x cos^2 x
所以1-sin^4 x-cos^4 x=2sin^2 x cos^2 x
因为
sin^6 x+cos^6 x
=(sin^2 x+cos^2 x)^3-3sin^4 x cos^2 x-3sin^2 x cos^4 x
=1-3sin^2 x cos^2 x(sin^2 x+cos^2 x)
=1-3sin^2 x cos^2 x
所以1-sin^6 x-cos^6 x=3sin^2 x cos^2 x
所以(1-sin^6 x-cos^6 x)/(1-sin^4 x-cos^4 x) =3sin^2 x cos^2 x/(2sin^2 x cos^2 x)=3/2

(1-sin^6 x-cos^6 x)/(1-sin^4 x-cos^4 x) =1

(1-sin^6 x-cos^6 x)/(1-sin^4 x-cos^4 x) =3