求值: 2(sin^6 θ+cos^6 θ)-3(sin^4 θ+cos^4 θ)

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求值:2(sin^6θ+cos^6θ)-3(sin^4θ+cos^4θ)求值:2(sin^6θ+cos^6θ)-3(sin^4θ+cos^4θ)求值:2(sin^6θ+cos^6θ)-3(sin^4θ

求值: 2(sin^6 θ+cos^6 θ)-3(sin^4 θ+cos^4 θ)
求值: 2(sin^6 θ+cos^6 θ)-3(sin^4 θ+cos^4 θ)

求值: 2(sin^6 θ+cos^6 θ)-3(sin^4 θ+cos^4 θ)
2(sin^6 θ+cos^6 θ)-3(sin^4 θ+cos^4 θ)
=2[(sin^2θ+cos^2θ)^3-3sin^2θcos^2θ(sin^2θ+cos^2θ)]-3[(sin^2θ+cos^2θ)^2-2sin^2θcos^2θ]
=2[1-3sin^2θcos^2θ]-3[1-2sin^2θcos^2θ]
=2-6sin^2θcos^2θ-3+6sin^2θcos^2θ
=-1