已知sinA+sinB=sin225°,cosA+cosB=cos225° 求cos(A-B）及cos(A+B)的值

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已知sinA+sinB=sin225°,cosA+cosB=cos225° 求cos(A-B）及cos(A+B)的值
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已知sinA+sinB=sin225°,cosA+cosB=cos225° 求cos(A-B）及cos(A+B)的值
已知sinA+sinB=sin225°,cosA+cosB=cos225° 求cos(A-B）及cos(A+B)的值

已知sinA+sinB=sin225°,cosA+cosB=cos225° 求cos(A-B）及cos(A+B)的值
先求两式的平方和,得2sinAsinB+2cosAcosB=-1,以后就简单了吧

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求得sinA*sinB和cosA*cosB即可；
(sinA+sinB)的平方+(cosA+cosB)的平方=2+2*(cosA*cosB+sinA*sinB)
左边根据sinA+sinB=sin225°,cosA+cosB=cos225°的条件代入数值，得：
cosA*cosB+sinA*sinB=-1/2=cos(A-B)

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