证明1/a+1/b=1/c,三个角比为1;2;4.
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三个角比为1：2：4.所对边应该是c，b，a，因为这样c是最小的。才有可能1/a+1/b=1/c
证：A+B+C=180, C:B:A=1:2:4, 得：C＝180/7, B=360/7, A=720/7
正弦定理：sinA/a=sinB/b=sinC/c = k
1/a=k/sinA, 1/b=k/sinB, 1/c=k/sinC
原题变为要证： 1/sinA + 1/sinB = 1/sinC
1/sinA+1/sinB=(sin360/7+sin720/7)/(sin360/7*sin720/7)
= 2sin540/7*cos180/7 / [sin360/7*sin(180-720/7)]
= 2cos180/7 / sin360/7 = 2 cos180/7 / [2sin180/7*cos180/7]
= 1/sin180/7 = 1/sinC 得证
