作业帮化简：sin^2a+sin^2(a-180/3)+sin^2(a+180/3)
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/29 11:31:01
化简：sin^2a+sin^2(a-180/3)+sin^2(a+180/3)
sin^2a+sin^2(a-180°/3)+sin^2(a+180°/3)
=1-cos2a+1-cos2(a-180°/3)+1-cos2(a+180°/3)
=3-cos2a-[cos2(a-180°/3)+cos2(a+180°/3)]
=3-cos2a-[cos(2a-120°)+cos(2a+120°)]
=3-cos2a-2cos2acos120°
=3-cos2a+2cos2acos60°
=3-cos2a+cos2a
=3
=1-cos2a+1-cos2(a-180°/3)+1-cos2(a+180°/3)
=3-cos2a-[cos2(a-180°/3)+cos2(a+180°/3)]
=3-cos2a-[cos(2a-120°)+cos(2a+120°)]
=3-cos2a-2cos2acos120°
=3-cos2a+2cos2acos60°
=3-cos2a+cos2a
=3
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