问题描述: (1-sin^6θ-cos^6θ)/(1-sin^4θ-cos^4θ) 1个回答 分类:数学 2014-11-19 问题解答: 我来补答 1-sin^6θ-cos^6θ=1-[(sin^2θ)^3+(cos^2θ)^3]=1-(sin^2θ+cos^2θ)(sin^4θ-sin^2θcos^2θ+cos^4θ)=1-(sin^4θ-sin^2θcos^2θ+cos^4θ)=1-(sin^4θ+2sin^2θcos^2θ+cos^4θ-3sin^2θcos^2θ)=1-[(sin^2θ+cos^2θ)^2-3sin^2θcos^2θ]=3sin^2θcos^2θ1-sin^4θ-cos^4θ=1-(sin^4θ+cos^4θ)=1-[(sin^4θ+2sin^2θcos^2θ+cos^4θ-2sin^2θcos^2θ)]=1-[(sin^2θ+cos^2θ)^2-2sin^2θcos^2θ]=2sin^2θcos^2θ所以:(1-sin^6θ-cos^6θ)/(1-sin^4θ-cos^4θ) =(3sin^2θcos^2θ)/(2sin^2θcos^2θ)=3/2. 展开全文阅读