化简sina^2+sinb^2+2sinasinbcos(a+b)

化简sina^2+sinb^2+2sinasinbcos(a+b)
化简sina^2+sinb^2+2sinasinbcos(a+b)

化简sina^2+sinb^2+2sinasinbcos(a+b)
不需要“积化和差”公式的证法：
sina^2+sinb^2+2sinasinbcos(a+b)
=sina^2+sinb^2+2sinasinb(cosacosb-sinasinb)
=sina^2+sinb^2+2sinasinbcosacosb-2(sina)^2(sinb)^2
=[sina^2-(sina)^2(sinb)^2]+[sinb^2-(sina)^2(sinb)]^2+2sinasinbcosacosb
=(sina)^2[1-(sinb)^2]+(sinb)^2[1-(sina)^2]+2sinasinbcosacosb
=(sina)^2(cosb)^2+(sinb)^2(cosa)^2+2sinasinbcosacosb
=(sinacosb+cosasinb)^2
=[sin(a+b)]^2.

[sin(a+b)cos(a-b)]^2+[(sina)^2-(sinb)^2]^2
不知道您满意否

sina^2+sinb^2+2sinasinbcos(a+b)
=1/2(1-cos2a)+1/2(1-cos2b)+(cos(a-b)-cos(a+b))*cos(a+b)
=1-1/2(cos2a+cos2b)+cos(a-b)*cos(a+b)-cos(a+b)^2
=1-1/2*2cos(a-b)*cos(a+b)+cos(a-b)*cos(a+b)-cos(a+b)^2
=1-cos(a+b)^2
=sin(a+b)^2

原式= sina^2+sinb^2+2sinasinb(cosacosb-sinasinb)
= sina^2+sinb^2+2sinacosasinbcosb-2(sinasinb)^2
= sina^2+sinb^2+0.5*4sinacosasinbcosb-2(sinasinb)^2
= sina^2+sinb^2+0.5sin2a*sin2b-2(sinasinb)^2

仔细观察一下式子您可以发现
其实，该式子是向量b=（sina,sin（-b）的模的公式，若是您正在做某一到题目的话，您可以把它转化过来
把它放到坐标系里看的话，即是角（a+b）所对的弦长，所以上几层楼的同志有的做错了