已知锐角abc满足sina+sinc=sinb,cosa-cosc=cosb,求a-b的值
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已知锐角abc满足sina+sinc=sinb,cosa-cosc=cosb,求a-b的值
![已知锐角abc满足sina+sinc=sinb,cosa-cosc=cosb,求a-b的值](/uploads/image/z/6692245-61-5.jpg?t=%E5%B7%B2%E7%9F%A5%E9%94%90%E8%A7%92abc%E6%BB%A1%E8%B6%B3sina%2Bsinc%3Dsinb%2Ccosa-cosc%3Dcosb%2C%E6%B1%82a-b%E7%9A%84%E5%80%BC)
sina+sinc=sinb
sina-sinb=-sinc
sin^a-2sinasinb+sin^b=sin^c (1)
cosa-cosc=cosb
cosa-cosb=cosc
cos^a-2cosacosb+cos^b=cos^c (2)
(1)+(2)
1-2(sinasinb+cosacosb)+1=1
1/2=cos(a-b)
a-b=60
sina-sinb=-sinc
sin^a-2sinasinb+sin^b=sin^c (1)
cosa-cosc=cosb
cosa-cosb=cosc
cos^a-2cosacosb+cos^b=cos^c (2)
(1)+(2)
1-2(sinasinb+cosacosb)+1=1
1/2=cos(a-b)
a-b=60
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