数学.在ABC中,角A.B.C的对边是a.b.c,已知sinC+cosC=1-sin(C/2)(1)求sinC的值.(2)若【a平方+b平方=4(a+b)-8】,求c边的值.
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![数学.在ABC中,角A.B.C的对边是a.b.c,已知sinC+cosC=1-sin(C/2)(1)求sinC的值.(2)若【a平方+b平方=4(a+b)-8】,求c边的值.](/uploads/image/z/1739297-65-7.jpg?t=%E6%95%B0%E5%AD%A6%EF%BC%8E%E5%9C%A8ABC%E4%B8%AD%2C%E8%A7%92A.B.C%E7%9A%84%E5%AF%B9%E8%BE%B9%E6%98%AFa.b.c%2C%E5%B7%B2%E7%9F%A5sinC%2BcosC%3D1-sin%EF%BC%88C%2F2%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82sinC%E7%9A%84%E5%80%BC%EF%BC%8E%EF%BC%882%EF%BC%89%E8%8B%A5%E3%80%90a%E5%B9%B3%E6%96%B9%2Bb%E5%B9%B3%E6%96%B9%3D4%EF%BC%88a%2Bb%EF%BC%89-8%E3%80%91%2C%E6%B1%82c%E8%BE%B9%E7%9A%84%E5%80%BC%EF%BC%8E)
数学.在ABC中,角A.B.C的对边是a.b.c,已知sinC+cosC=1-sin(C/2)(1)求sinC的值.(2)若【a平方+b平方=4(a+b)-8】,求c边的值.
数学.在ABC中,角A.B.C的对边是a.b.c,已知sinC+cosC=1-sin(C/2)
(1)求sinC的值.(2)若【a平方+b平方=4(a+b)-8】,求c边的值.
数学.在ABC中,角A.B.C的对边是a.b.c,已知sinC+cosC=1-sin(C/2)(1)求sinC的值.(2)若【a平方+b平方=4(a+b)-8】,求c边的值.
1
sinC+cosC=1-sin(C/2)
2sin(C/2)cos(C/2)=2sin²(C/2)-sin(C/2)
∵sin(C/2)≠0
∴2cos(C/2)=2sin(C/2)-1
sin(C/2)-cos(C/2)=1/2
[sin(C/2)-cos(C/2)]^2=1/4
1-sinC=1/4,
sinC=3/4
2
∵a^2+b^=4(a+b)-8
∴(a-2)^2+(b-2)^2=0
∴a=2,b=2
∵sin(C/2)-cos(C/2)=1/2
∴[sin(C/2)+cos(C/2)]^2=1+3/4=7/4
∴sin(C/2)+cos(C/2)=√7/2
∴sin(C/2)=(√7+1)/4
∴cosC=1-sin(C/2)-sinC=1/4-sin(C/2)=-√7/4
∴c^2=a^2+b^2-2abcosC=8+2√7
∴c=1+√7
(1)sinC+cosC=1-sin(C/2)
2sin(C/2)cos(C/2)=2sin²(C/2)-sin(C/2)
∵sin(C/2)≠0
∴2cos(C/2)=2sin(C/2)-1
sin(C/2)-cos(C/2)=1/2
[sin(C/2)-cos(C/2)]^2=1/4
1-sinC=1/4,
sinC=...
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(1)sinC+cosC=1-sin(C/2)
2sin(C/2)cos(C/2)=2sin²(C/2)-sin(C/2)
∵sin(C/2)≠0
∴2cos(C/2)=2sin(C/2)-1
sin(C/2)-cos(C/2)=1/2
[sin(C/2)-cos(C/2)]^2=1/4
1-sinC=1/4,
sinC=3/4
(2)∵a^2+b^=4(a+b)-8
∴(a-2)^2+(b-2)^2=0
∴a=2,b=2
∵sin(C/2)-cos(C/2)=1/2
∴[sin(C/2)+cos(C/2)]^2=1+3/4=7/4
∴sin(C/2)+cos(C/2)=√7/2
∴sin(C/2)=(√7+1)/4
∴cosC=1-sin(C/2)-sinC=1/4-sin(C/2)=-√7/4
∴c^2=a^2+b^2-2abcosC=8+2√7
∴c=1+√7
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