sina+sinb=1,cosa+cosb=0,求cos(a+b)=?
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sina+sinb=1,cosa+cosb=0,求cos(a+b)=?
题目没有错吗
sina+sinb=1 , sin^2a+2sinasinb+sin^2b=1-----------------(1)
cosa+cosb=0, cos^2a+2cosacosb+cos^2b=0--------------(2)
(1)+(2)
2+2cos(a-b)=1 , cos(a-b)=-1/2
cos(a+b)=cosa...
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sina+sinb=1 , sin^2a+2sinasinb+sin^2b=1-----------------(1)
cosa+cosb=0, cos^2a+2cosacosb+cos^2b=0--------------(2)
(1)+(2)
2+2cos(a-b)=1 , cos(a-b)=-1/2
cos(a+b)=cosacosb-sinasinb
=-cos^2b-sinb(1-sinb)=-cos^2b-sinb+sin^2b=2sin^2b-sinb-1=(2sinb+1)(sinb-1)
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我给你个提示吧,cosa+cosb=0,所以a=(2k+1)π+b
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