求1-cos^6x-sin^6x/1-cos^4x-sin^4x的值,
问题描述：
求1-cos^6x-sin^6x/1-cos^4x-sin^4x的值,
答
(1-cos^6x-sin^6x)/(1-cos^4x-sin^4x)
=[1-(cos^6x+sin^6x)]/[1-(cos^4x-sin^4x)]
=[1-(cos^2x+sin^2x)(cos^4x-cos^2xsin^2x+sin^4x)]/[1-(cos^2x-sin^2x)(cos^2x+sin^2x)]
=[1-(cos^4x-cos^2xsin^2x+sin^4x)]/[1-(cos^2x-sin^2x)]
=[1-(cos^4x+2cos^2xsin^2x+sin^4x-3cos^2xsin^2x)]/[1-cos^2x+sin^2x]
={1-[(cos^2x+sin^2x)^2-3cos^2xsin^2x]}/[sin^2x+sin^2x]
={1-[1-3cos^2xsin^2x]}/(2sin^2x)
=(1-1+3cos^2xsin^2x)/(2sin^2x)
=3cos^2xsin^2x/(2sin^2x)
=3cos^2x/2看不太懂这么复杂吗用平方差和立方差