化简sin(a-b)sina+cos(a-b)cosa答案为COSB,

化简sin(a-b)sina+cos(a-b)cosa答案为COSB,
化简sin(a-b)sina+cos(a-b)cosa
答案为COSB,

化简sin(a-b)sina+cos(a-b)cosa答案为COSB,
因为 cos(a-b -a)= cos(a-b)cosa +sin(a-b)sina
所以 sin(a-b)sina+cos(a-b)cosa =cos(a-b-a)=cos(-b) =cosb

利用和角公式
cos(x-y)=cosxcosy+sinxsiny
令x=a-b,y=a
我们得到
sin(a-b)sina+cos(a-b)cosa=cos(a-b-a)=cos(-b)=cos b,
因为cosx是偶函数

sin(a-B)cosa-1/2[sin(2a+B)-sinB] =[sin(a-B+a)+sin(a-B-a=cos2asin(-B) =-cos2asinB cos(a-¦Ð/6)+sina=4¡Ì3/5 cos(-¦Ð/6+

=(sinacosb-sinbcosa)sina+(cosacosb+sinasinb)cosa
=sina²cosb-sinasinbcosa+cosa²cosb+sinasinbcosa
=（sina²+cosa²）cosb
=1·cosb
即=cosb

这个就是逆用公式，
cosAcoB+sinAsinB=cos(A-B)
所以 sin(a-b)sina+cos(a-b)cosa=cos [a-(a-b)]=cosb
(整体思想，将a-b看成1个新的角)