百度作业网求（1-sin^6α-cos^6α)/(1-sin^4α-cos^4α)的值.
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/06/22 22:06:29
求（1-sin^6α-cos^6α)/(1-sin^4α-cos^4α)的值.
（1-sin^6α-cos^6α)/(1-sin^4α-cos^4α)
=[1-(sin^2 a+cos^2a)(sin^4 a+cos^4 a-sin^2 acos^2 a)]/[1-(sin^2 a+cos^2a)^2+2sin^2 acos^2 a]
=[1-(sin^4 a+cos^4 a-sin^2 acos^2 a)]/[2sin^2 acos^2 a]
=[1-(sin^2 a+cos^2 a)^2+2sin^2 acos^2 a+sin^2 acos^2 a)]/[2sin^2 acos^2 a]
=3sin^2 acos^2 a/[2sin^2 acos^2 a]
=3/2
=[1-(sin^2 a+cos^2a)(sin^4 a+cos^4 a-sin^2 acos^2 a)]/[1-(sin^2 a+cos^2a)^2+2sin^2 acos^2 a]
=[1-(sin^4 a+cos^4 a-sin^2 acos^2 a)]/[2sin^2 acos^2 a]
=[1-(sin^2 a+cos^2 a)^2+2sin^2 acos^2 a+sin^2 acos^2 a)]/[2sin^2 acos^2 a]
=3sin^2 acos^2 a/[2sin^2 acos^2 a]
=3/2
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