已知sina+sinb=1/2 cosa-cosb=1/3.请问cos(a+b)等于多少?
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已知sina+sinb=1/2 cosa-cosb=1/3.请问cos(a+b)等于多少?
![已知sina+sinb=1/2 cosa-cosb=1/3.请问cos(a+b)等于多少?](/uploads/image/z/3856272-24-2.jpg?t=%E5%B7%B2%E7%9F%A5sina%2Bsinb%3D1%2F2+cosa-cosb%3D1%2F3.%E8%AF%B7%E9%97%AEcos%28a%2Bb%29%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
sina+sinb=1/2 cosa-cosb=1/3
分别平分得
(sina+sinb)^2=sin^2a+2sinasinb+sin^2b=1/4 1
(cosa-cosb)^2=cos^2a-2cosacosb+cos^2b=1/9 2
1式+2式得
sin^2a+2sinasinb+sin^2b+cos^2a-2cosacosb+cos^2b=1/4+1/9
2-2(cosacosb-sinasinb)=13/36
2cos(a+b)=2-13/36=59/36
cos(a+b)=59/72
分别平分得
(sina+sinb)^2=sin^2a+2sinasinb+sin^2b=1/4 1
(cosa-cosb)^2=cos^2a-2cosacosb+cos^2b=1/9 2
1式+2式得
sin^2a+2sinasinb+sin^2b+cos^2a-2cosacosb+cos^2b=1/4+1/9
2-2(cosacosb-sinasinb)=13/36
2cos(a+b)=2-13/36=59/36
cos(a+b)=59/72
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