化简sin^6 a+cos^6 a+3sin^2 acos^2a
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/05 05:46:44
化简sin^6 a+cos^6 a+3sin^2 acos^2a
注意是6次方不是6倍a
三角函数一看就烦 请达人指导
注意是6次方不是6倍a
三角函数一看就烦 请达人指导
sin^6 a+cos^6 a+3sin^2 acos^2a
=(sin^2 a+cos^2 a)(sin^4 a+cos^4 a-sin^2 acos^2 a)
+3sin^2 acos^2a
=sin^4 a+cos^4 a-sin^2 acos^2 a+3sin^2 acos^2a
=sin^4 a+cos^4 a+2sin^2 acos^2 a
=(sin^2 a+cos^2 a)^2
=1
=(sin^2 a+cos^2 a)(sin^4 a+cos^4 a-sin^2 acos^2 a)
+3sin^2 acos^2a
=sin^4 a+cos^4 a-sin^2 acos^2 a+3sin^2 acos^2a
=sin^4 a+cos^4 a+2sin^2 acos^2 a
=(sin^2 a+cos^2 a)^2
=1
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