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

题目

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

答案

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+6...