题目

(1-cos^4X-sin^4x)∕(1-cos^6x-sin^6x)=
化简(急)

提问时间：2021-02-20

答案

1-cos^4x-sin^4x
=1-(cos^4x+sin^4x)
=1-[(cos^2x+sin^2x)^2-2cos^2xsin^2x]
=1-(1-2cos^2xsin^2x)
=2cos^2xsin^2x
1-cos^6x-sin^6x
=1-(cos^2x+sin^2x)(cos^4x-cos^2xsin^2x+sin^4x)
=1-[(cos^2x+sin^2x)^2-3cos^2xsin^2x]
=1-[1-3cos^2xsin^2x]
=3cos^2xsin^2x
原式=2cos^2xsin^2x/3cos^2xsin^2x=2/3