已知5cos(a-b/2)+7caos(b/2)=0 求(tan a/2)*tan((a-b)/2)
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已知5cos(a-b/2)+7caos(b/2)=0 求(tan a/2)*tan((a-b)/2)
![已知5cos(a-b/2)+7caos(b/2)=0 求(tan a/2)*tan((a-b)/2)](/uploads/image/z/18591275-11-5.jpg?t=%E5%B7%B2%E7%9F%A55cos%28a-b%2F2%29%2B7caos%28b%2F2%29%3D0+%E6%B1%82%28tan+a%2F2%29%2Atan%28%28a-b%29%2F2%29)
5cos(a-b/2)+7cos(b/2)=5cosacos(b/2)+5sinasin(b/2)+7cos(b/2)
=10cos(a/2)cos[(a-b)/2]+2cos(b/2)=0
cos(a/2)cos[(a-b)/2]=(-1/5)*2cos(b/2) (1)
又5cos(a-b/2)+7cos(b/2)=5cosacos(b/2)+5sinasin(b/2)+7cos(b/2)
=-10sin(a/2)sin[(a-b)/2]+12cos(b/2)=0
sin(a/2)sin[(a-b)/2]=(6/5)*cos(b/2) (2)
(2)/(1) 得(tan a/2)*tan((a-b)/2) =(6/5)*cos(b/2)÷[(-1/5)*2cos(b/2)]
=-6
=10cos(a/2)cos[(a-b)/2]+2cos(b/2)=0
cos(a/2)cos[(a-b)/2]=(-1/5)*2cos(b/2) (1)
又5cos(a-b/2)+7cos(b/2)=5cosacos(b/2)+5sinasin(b/2)+7cos(b/2)
=-10sin(a/2)sin[(a-b)/2]+12cos(b/2)=0
sin(a/2)sin[(a-b)/2]=(6/5)*cos(b/2) (2)
(2)/(1) 得(tan a/2)*tan((a-b)/2) =(6/5)*cos(b/2)÷[(-1/5)*2cos(b/2)]
=-6
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