正玄定理 sinB/(sinA + sinC) = tan(B/2)
萬(wàn)能公式sinB = 2tan(B/2) / (1+tan^2 (B/2));
和差化積 sin A+sinC=2sin[(A+C)/2]·cos[(A-C)/2] = 2 cos(B/2)*cos[(A-C)/2]
帶入消掉 tan(B/2) != 0
2 = (1+tan^2 (B/2)) * 2 cos(B/2)*cos[(A-C)/2]
1 = cos[(A-C)/2] / cos (B/2)
cos [(A-C)/2] = cos(B/2)
再用和差化積 cos α-cos β=-2sin[(α+β)/2]·sin[(α-β)/2]
sin(((A-C)/2 + B/2)/2) = 0 或者是 sin(((A-C)/2 - B/2)/2) = 0
A+B-C = 180 - 2C,于是有sin ((90-C)/2) = 0 或者是 sin ((A-90)/2) = 0
考查范圍,有C=90或者A=90 直角三角形.
b/(a+c)=tan（B/2）
b/(a+c)=tan（B/2）
判斷三角形ABC的形狀.
判斷三角形ABC的形狀.
數(shù)學(xué)人氣：255 ℃時(shí)間：2020-09-09 06:27:03
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