证明公式cos(a-b)=cosacosb sinasinb
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![证明公式cos(a-b)=cosacosb sinasinb](/uploads/image/f/7269916-4-6.jpg?t=%E8%AF%81%E6%98%8E%E5%85%AC%E5%BC%8Fcos%28a-b%29%3Dcosacosb+sinasinb)
化简cos(a+b)cosa+sin(a+b)sina=cos[(a+b)-a]=cosbcos(31°-a)cos(29°+a)-cos(59°+a)cos(61°-a)=cos(31°-a)cos
2sinasinb=cos(a-b)-cos(a+b)2sinasinb=cosacob+sinasinb-cosacosb+sinasinb2sinasinb=2sinasinb所以2sinA*si
(sinA+sinB)/(cosA+cosB)=2sin(A+B)/2*cos(A-B)/cos2/cos(A+B)/2*cosA-B)/2=sin(A+B)/2/cos(A+B)/2=tan(A+B
cos(A-B)cos(B-C)cos(C-A)=1由于函数的余弦cosx的值域是【-1,1】也是就说任意角的余弦值都是小于等于0的只有当x=0或者2kπ时取最大值所以等式cos(A-B)cos(B-
cos(a-b)=cosacosb+sinasinb(1)cos(a+b)=cosacosb-sinasinb(2)(1)-(2)cos(a-b)-cos(a+b)=2sinasinbsinasinb
e^ia=cosa+isina,e^ia*e^ib=e^i(a+b),(cosa+isina)(cosb+isinb)=cos(a+b)+isin(a+b),(cosacosb-sinasinb)+i
cosa-cosb=-2*cos(a+b)/2*sin(a-b)/2|cosa-cosb|=2*|cos(a+b)/2|*|sin(a-b)/2|≤2|sin(a-b)/2|又:sinx≤x所以sin
证:∵右边=(1/2)[(cosacosb-sinasinb)+cosacosn+sinasinb)].右边=(1/2)(2cosacosb)=cosacosb.左=右.证毕.注:三角形函数的证明离不
1:证明Cos(П/2-a)=Sina:Cos(П/2-a)=cos(π/2)cosa+sin(π/2)sina=0*cosa+1*sina=sina2:证明Cos(2П-a)=Cosa:Cos(2П
cos(3π/2-a)=cos3π/2cosa+sin3π/2sina=0·cosa+(-1)sina=-sina同理,有:sin(3π/2-a)=sin3π/2cosa-cos3π/2sina=-c
cosAcosB+sinAsinB
cos(a+3π)=cos(2π+π+a)根据cos(2π+a)=cos(a)所以cos(a+3π)=cos(2π+π+a)=cos(π+a)根据奇变偶不变符号看象限的原理可知cos(π+a)=-co
http://hi.baidu.com/wolf224/blog/item/296fec120385450a5aaf53c7.html
cos(2π-a)=cos2πcosa+sin2πsina=1×cosa+0×sina=cosa
可以向量!用向量只考虑cos在12限的夹角
a·b=x1·x2+y1·y2|a||b|cosθ=|a||b|*(|a|^2+|b|^2-(y1-y2)^2-(x1-x2)^2)/2|a||b|=(x1^2+y1^2+x2^2+y2^2-x1^2
∵cosx=(e^ix+e^-ix)/2e^ix=cosx+isinx∴cos(a+b)=[e^i(a+b)+e^-i(a+b)]/2=[(cosa+isina)(cosb+isinb)+(cosa-