△ABC中a,b,c是内角A,B,C的对边,且lgsinA,lgsinB,lgsinC成等差数列则下列直线l₁:(sin²A)x+(sinA)y-a=0l₂:(sin²B)x+(sinC)y-c=0的位置关系如何?为什么lg(sinAsinC)=lg(sinB)²
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 01:50:30
![△ABC中a,b,c是内角A,B,C的对边,且lgsinA,lgsinB,lgsinC成等差数列则下列直线l₁:(sin²A)x+(sinA)y-a=0l₂:(sin²B)x+(sinC)y-c=0的位置关系如何?为什么lg(sinAsinC)=lg(sinB)²](/uploads/image/z/11473556-68-6.jpg?t=%E2%96%B3ABC%E4%B8%ADa%2Cb%2Cc%E6%98%AF%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%2C%E4%B8%94lgsinA%2ClgsinB%2ClgsinC%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E5%88%99%E4%B8%8B%E5%88%97%E7%9B%B4%E7%BA%BFl%26%238321%3B%3A%28sin%26sup2%3BA%29x%2B%28sinA%29y-a%3D0l%26%238322%3B%3A%28sin%26sup2%3BB%29x%2B%28sinC%29y-c%3D0%E7%9A%84%E4%BD%8D%E7%BD%AE%E5%85%B3%E7%B3%BB%E5%A6%82%E4%BD%95%3F%E4%B8%BA%E4%BB%80%E4%B9%88lg%28sinAsinC%29%3Dlg%28sinB%29%26sup2)
△ABC中a,b,c是内角A,B,C的对边,且lgsinA,lgsinB,lgsinC成等差数列则下列直线l₁:(sin²A)x+(sinA)y-a=0l₂:(sin²B)x+(sinC)y-c=0的位置关系如何?为什么lg(sinAsinC)=lg(sinB)²
△ABC中a,b,c是内角A,B,C的对边,且lgsinA,lgsinB,lgsinC
成等差数列则下列直线l₁:(sin²A)x+(sinA)y-a=0
l₂:(sin²B)x+(sinC)y-c=0
的位置关系如何?
为什么lg(sinAsinC)=lg(sinB)²
△ABC中a,b,c是内角A,B,C的对边,且lgsinA,lgsinB,lgsinC成等差数列则下列直线l₁:(sin²A)x+(sinA)y-a=0l₂:(sin²B)x+(sinC)y-c=0的位置关系如何?为什么lg(sinAsinC)=lg(sinB)²
因sinA,sinB,sinC均大于零
lg(sinA)+lg(sinC)=2lg(sinB)
lg(sinAsinC)=lg(sinB)^2
sinAsinC=(sinB)^2
L1斜率k1=-sinA
L2斜率k2=-sinB^2/sinC=-sinA
首先,两直线平行
取一特殊点,当x=0时,y1=a/sinA
y2=c/sinC
所以y1=y2
两直线重合
lgsinA,lgsinB,lgsinC成等差数列
所以:lgsinA+lgsinC=2*lgsinB
所以:sinA*sinC=sinB^2
l₁:(sin²A)x+(sinA)y-a=0的斜率为:K1=-sinA
l₂:(sin²B)x+(sinC)y-c=0的斜率为:K2=-sinB^2/sinC
K1/K2=1
所以他们为平行~