化简

问题描述:

化简
(1)根号(1-sin²2)
(2)(1-cos^4 x-sin^4 x)/(1-cos^6 x-sin^6 x)
(1)-cos2 (2)2/3

1.根号(1-sin²2)=-cos2
2.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答案不是3/2是2/3因为cos2<0(2不是度是弧度) 为上面所做的解释。是滴,我自己写错了分母跟分子我写错了,上面化简是对的