怎么证明两角和的余弦公式 Cos(x+y)=CosxCosy-SinxSiny这个我看不懂!第一个公式的证明:右边=2*sin[(A+B)/2]*cos[(A-B)/2]=2*[sin(A/2)*cos(B/2)+cos(A/2)sin(B/2)]*[cos(A/2)cos(B/2)+sin(A/2)sin(B/2)]=2*sin(A/2)*cos(A/2)*cos(B/2)*cos(
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/17 02:16:19
![怎么证明两角和的余弦公式 Cos(x+y)=CosxCosy-SinxSiny这个我看不懂!第一个公式的证明:右边=2*sin[(A+B)/2]*cos[(A-B)/2]=2*[sin(A/2)*cos(B/2)+cos(A/2)sin(B/2)]*[cos(A/2)cos(B/2)+sin(A/2)sin(B/2)]=2*sin(A/2)*cos(A/2)*cos(B/2)*cos(](/uploads/image/z/3938971-67-1.jpg?t=%E6%80%8E%E4%B9%88%E8%AF%81%E6%98%8E%E4%B8%A4%E8%A7%92%E5%92%8C%E7%9A%84%E4%BD%99%E5%BC%A6%E5%85%AC%E5%BC%8F+Cos%28x%2By%29%3DCosxCosy-SinxSiny%E8%BF%99%E4%B8%AA%E6%88%91%E7%9C%8B%E4%B8%8D%E6%87%82%21%E7%AC%AC%E4%B8%80%E4%B8%AA%E5%85%AC%E5%BC%8F%E7%9A%84%E8%AF%81%E6%98%8E%3A%E5%8F%B3%E8%BE%B9%3D2%2Asin%5B%28A%2BB%29%2F2%5D%2Acos%5B%28A-B%29%2F2%5D%3D2%2A%5Bsin%28A%2F2%29%2Acos%28B%2F2%29%2Bcos%28A%2F2%29sin%28B%2F2%29%5D%2A%5Bcos%28A%2F2%29cos%28B%2F2%29%2Bsin%28A%2F2%29sin%28B%2F2%29%5D%3D2%2Asin%28A%2F2%29%2Acos%28A%2F2%29%2Acos%28B%2F2%29%2Acos%28)
$ P) \ PB%$pR0>U;:Y(yV7F<2:^9EX3+FΤt|`TxF=[C<7:hJouߐ6^S4C^jS%fȀ!#!WF{]{lǰr,s/k怎么证明两角和的余弦公式 Cos(x+y)=CosxCosy-SinxSiny这个我看不懂!第一个公式的证明:右边=2*sin[(A+B)/2]*cos[(A-B)/2]=2*[sin(A/2)*cos(B/2)+cos(A/2)sin(B/2)]*[cos(A/2)cos(B/2)+sin(A/2)sin(B/2)]=2*sin(A/2)*cos(A/2)*cos(B/2)*cos(
怎么证明两角和的余弦公式 Cos(x+y)=CosxCosy-SinxSiny
这个我看不懂!
第一个公式的证明:
右边=2*sin[(A+B)/2]*cos[(A-B)/2]
=2*[sin(A/2)*cos(B/2)+cos(A/2)sin(B/2)]*[cos(A/2)cos(B/2)+sin(A/2)sin(B/2)]
=2*sin(A/2)*cos(A/2)*cos(B/2)*cos(B/2)+2*cos(A/2)*cos(A/2)*sin(B/2)*cos(B/2)+2*sin(A/2)*sin(A/2)*cos(B/2)*sin(B/2)+2*sin(A/2)*cos(A/2)*sin(B/2)*sin(B/2)
=sinA*[cos(B/2)*cos(B/2)+sin(B/2)*sin(B/2)]+sin(B/2)*[cos(B/2)*cos(B/2)+sin(B/2)*sin(B/2)]
=sinA+sinB=左边
证毕
其中用到公式:
sinA=2*sin(A/2)*cos(A/2),sinB=2*cos(B/2)*sin(B/2)
cos(B/2)*cos(B/2)+sin(B/2)*sin(B/2)=1
其他的公式依此类推,自己推推看吧!
谁能说个好懂的怎么证明两角和的余弦公式 Cos(x+y)=CosxCosy-SinxSiny这个我看不懂!第一个公式的证明:右边=2*sin[(A+B)/2]*cos[(A-B)/2]=2*[sin(A/2)*cos(B/2)+cos(A/2)sin(B/2)]*[cos(A/2)cos(B/2)+sin(A/2)sin(B/2)]=2*sin(A/2)*cos(A/2)*cos(B/2)*cos(
怎么证明两角和的余弦公式 Cos(x+y)=CosxCosy-SinxSiny
那个答案谁写的?怎么用后面的公式,证前面的结论了.
这个证明方法应该是解析法因为是任意角,这个公式和cos(y-x)=cosycosx+sinysinx完全等价的,用向量证明,任意两向量(x1,y1),(x2,y2)它们与横轴正轴夹角为X,Y,根据向量夹角公式cos(Y-X)=(x1x2+y1y2)/(1向量的模乘2向量的模),然后化开,结合图像x1比上1向量的模乘以x2比2向量的模=sinXsinY,同理…所以公式得证,x1,x2 ,y1,y2,X,Y都是任意实数...
全部展开
因为是任意角,这个公式和cos(y-x)=cosycosx+sinysinx完全等价的,用向量证明,任意两向量(x1,y1),(x2,y2)它们与横轴正轴夹角为X,Y,根据向量夹角公式cos(Y-X)=(x1x2+y1y2)/(1向量的模乘2向量的模),然后化开,结合图像x1比上1向量的模乘以x2比2向量的模=sinXsinY,同理…所以公式得证,x1,x2 ,y1,y2,X,Y都是任意实数
收起