化简三角函数.1-cos^4α-sin^4α/1-cos^6α-sin6α 我这里没加括号呀。

没加括号的话sin^4α/1根本就没用的嘛~
应该是(1-cos^4α-sin^4α)/(1-cos^6α-sin^6α)
1=sin^2α+cos^2α
原式=(sin^2α+cos^2α-cos^4α-sin^4α)/(sin^2α+cos^2α-cos^6α-sin^6α)
分子=sin^2α(1-sin^2α)+cos^2α(1-cos^2α)=2sin^2αcos^2α
分母=sin^2α(1-sin^4α)+cos^2α(1-cos^4α)
sin^2α(1-sin^4α)=sin^2α(1-sin^2α)(1+sin^2α)=sin^2αcos^2α(1+sin^2α)
同理cos^2α(1-cos^4α)=sin^2αcos^2α(1+cos^2α)
原式=2sin^2αcos^2α/sin^2αcos^2α(1+sin^2α+1+cos^2α)=2/3