怎样证明余弦定理 余弦定理怎么证明?
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a^2=b^2+c^2-2*b*c*CosA
b^2=a^2+c^2-2*a*c*CosB
c^2=a^2+b^2-2*a*b*CosC
CosC=(a^2+b^2-c^2)/2ab
CosB=(a^2+c^2-b^2)/2ac
CosA=(c^2+b^2-a^2)/2bc
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\u2235a=b-c
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\u518d\u62c6\u5f00\uff0c\u5f97a^2=b^2+c^2-2*b*c*CosA
\u540c\u7406\u53ef\u8bc1\u5176\u4ed6\uff0c\u800c\u4e0b\u9762\u7684CosA=(c^2+b^2-a^2)/2bc\u5c31\u662f\u5c06CosA\u79fb\u5230\u53f3\u8fb9\u8868\u793a\u4e00\u4e0b\u3002
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\u5219\u6709BD=cosB*c\uff0cAD=sinB*c\uff0cDC=BC-BD=a-cosB*c
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AC^2=AD^2+DC^2
b^2=(sinB*c)^2+(a-cosB*c)^2
b^2=sin^2B*c^2+a^2+cos^2B*c^2-2ac*cosB
b^2=(sin^2B+cos^2B)*c^2-2ac*cosB+a^2
b^2=c^2+a^2-2ac*cosB
cosB=(c^2+a^2-b^2)/2ac
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用向量 (AB向量)=(AC向量)—(AB向量) 等式两边同时平方 再整理一下 OVER!
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绛旓細姝e鸡瀹氱悊鍏紡銆浣欏鸡瀹氱悊鍏紡 涓銆佹寮﹀畾鐞嗗叕寮 a/sinA=b/sinB=c/sinC=2R銆傘愭敞1銆戝叾涓淩鈥濅负涓夎褰⑩柍ABC澶栨帴鍦嗗崐寰勩備笅鍚屻傘愭敞2銆戞寮﹀畾鐞嗛傜敤浜庢墍鏈変笁瑙掑舰銆傚垵涓暟瀛︿腑锛屼笁瑙掑舰鍐呰鐨勬寮﹀肩瓑浜庘滃姣旀枩鈥濅粎閫傜敤浜庣洿瑙掍笁瑙掑舰銆備簩銆佹寮﹀畾鐞嗘帹璁哄叕寮 1銆侊紙1锛塧=2RsinA锛涳紙2锛塨=2RsinB锛涳紙3...
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