三角恒等变换的化简sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B=sinAsinB2sin²Asin²B-2sinAcosBsinBcosA=sinAsinB怎么化简的?接着上面的cosAcosB-sinAsinB=-1/2cos(A+B)=-1/2怎么化简的?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 16:28:41
![三角恒等变换的化简sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B=sinAsinB2sin²Asin²B-2sinAcosBsinBcosA=sinAsinB怎么化简的?接着上面的cosAcosB-sinAsinB=-1/2cos(A+B)=-1/2怎么化简的?](/uploads/image/z/8946638-62-8.jpg?t=%E4%B8%89%E8%A7%92%E6%81%92%E7%AD%89%E5%8F%98%E6%8D%A2%E7%9A%84%E5%8C%96%E7%AE%80sin%26%23178%3BA%2Bsin%26%23178%3BB-sin%26%23178%3BAcos%26%23178%3BB-2sinAcosBcosAsinB-cos%26%23178%3BAsin%26%23178%3BB%3DsinAsinB2sin%26%23178%3BAsin%26%23178%3BB-2sinAcosBsinBcosA%3DsinAsinB%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E7%9A%84%3F%E6%8E%A5%E7%9D%80%E4%B8%8A%E9%9D%A2%E7%9A%84cosAcosB-sinAsinB%3D-1%2F2cos%28A%2BB%29%3D-1%2F2%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E7%9A%84%EF%BC%9F)
三角恒等变换的化简sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B=sinAsinB2sin²Asin²B-2sinAcosBsinBcosA=sinAsinB怎么化简的?接着上面的cosAcosB-sinAsinB=-1/2cos(A+B)=-1/2怎么化简的?
三角恒等变换的化简
sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B=sinAsinB
2sin²Asin²B-2sinAcosBsinBcosA=sinAsinB
怎么化简的?
接着上面的cosAcosB-sinAsinB=-1/2
cos(A+B)=-1/2
怎么化简的?
三角恒等变换的化简sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B=sinAsinB2sin²Asin²B-2sinAcosBsinBcosA=sinAsinB怎么化简的?接着上面的cosAcosB-sinAsinB=-1/2cos(A+B)=-1/2怎么化简的?
sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B
=(sin²A-sin²Acos²B)-2sinAcosBcosAsinB+(sin²B-cos²Asin²B)
=sin²A(1-cos²B)-2sinAcosBcosAsinB+sin²B(1-cos²A)
=sin²Asin²B-2sinAcosBcosAsinB+sin²Bsin²A
=2sin²Asin²B-2sinAcosBsinBcosA
=2sinAsinB(sinAsinB-cosBcosA)
=2sinAsinB[-cos(B+A)]
=2sinAsinBcosC
∵sin²A+sin²B-sin²Acos²B-2sinAcosBcosAsinB-cos²Asin²B=sinAsinB
∴2sinAsinBcosC=sinAsinB
∴cosC=1/2,
∴C=60°