化简sin(啊尔法+贝塔)cos啊尔法-1/2[sin(2啊尔法+贝塔)-sin贝塔]
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/11/06 08:17:01
化简sin(啊尔法+贝塔)cos啊尔法-1/2[sin(2啊尔法+贝塔)-sin贝塔]
解由sin(α+β)cosα-1/2[sin(2α+β)-sinβ]
=sin(α+β)cosα-1/2[sin(α+β+α)-sinβ]
=sin(α+β)cosα-1/2[sin(α+β+α)-sinβ]
=sin(α+β)cosα-1/2[sin(α+β)cosα+cos(α+β)sinα-sinβ]
=sin(α+β)cosα-1/2sin(α+β)cosα-1/2cos(α+β)sinα+1/2sinβ
=1/2sin(α+β)cosα-1/2cos(α+β)sinα+1/2sinβ
=1/2[sin(α+β)cosα-cos(α+β)sinα]+1/2sinβ
=1/2sin(α+β-β)+1/2sinβ
=1/2sin(α)+1/2sinβ
=sin(α+β)cosα-1/2[sin(α+β+α)-sinβ]
=sin(α+β)cosα-1/2[sin(α+β+α)-sinβ]
=sin(α+β)cosα-1/2[sin(α+β)cosα+cos(α+β)sinα-sinβ]
=sin(α+β)cosα-1/2sin(α+β)cosα-1/2cos(α+β)sinα+1/2sinβ
=1/2sin(α+β)cosα-1/2cos(α+β)sinα+1/2sinβ
=1/2[sin(α+β)cosα-cos(α+β)sinα]+1/2sinβ
=1/2sin(α+β-β)+1/2sinβ
=1/2sin(α)+1/2sinβ
化简sin(啊尔法+贝塔)cos啊尔法-1/2[sin(2啊尔法+贝塔)-sin贝塔]
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