化简cos^2(a+15)+sin^2(a-15))+sin(a+180)cos(a-180)=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa=1-sin2a*sin30+(1/2)*sin2a=1-(1/2)*sin2a+(1/2)*sin2a=1 第一步到第二步是怎么来的

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 20:49:14
化简cos^2(a+15)+sin^2(a-15))+sin(a+180)cos(a-180)=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa=1-sin2a*sin30+(1/2)*sin2a=1-(1/2)*sin2a+(1/2)*sin2a=1 第一步到第二步是怎么来的

化简cos^2(a+15)+sin^2(a-15))+sin(a+180)cos(a-180)=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa=1-sin2a*sin30+(1/2)*sin2a=1-(1/2)*sin2a+(1/2)*sin2a=1 第一步到第二步是怎么来的
化简cos^2(a+15)+sin^2(a-15))+sin(a+180)cos(a-180)
=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa
=1-sin2a*sin30+(1/2)*sin2a
=1-(1/2)*sin2a+(1/2)*sin2a
=1
第一步到第二步是怎么来的

化简cos^2(a+15)+sin^2(a-15))+sin(a+180)cos(a-180)=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa=1-sin2a*sin30+(1/2)*sin2a=1-(1/2)*sin2a+(1/2)*sin2a=1 第一步到第二步是怎么来的
余弦二倍角公式：Cos2a=1-2Sina^2=2Cosa^2-1
正弦二倍角公式：sin2α = 2cosαsinα
所以
[2sinacos15°]*[2cosa*sin(-15°)]
=(2sinacosa)*(-2sin15°cos15°)
=-sin2asin30°
=-(1/2)*sin2a
看不懂是因为,你给出的解题过程有省略,详细如下：
cos^2(a+15)+sin^2(a-15)+sin(a+180)cos(a-180)
=cos^2(a+15)+sin^2(a+15)-sin^2(a+15)+sin^2(a-15)+sinacosa
=1+[sin^2(a-15)-sin^2(a+15)]+sinacosa
=1+[sin(a-15)+sin(a+15)][sin(a-15)-sin(a+15)]+sinacosa
=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa
=1-sin2a*sin30+(1/2)*sin2a
=1-(1/2)*sin2a+(1/2)*sin2a
=1

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