设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0

设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0
设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0

设直线ax+by+c的倾角为a,sina+cosa=0,则a,b满足?a-b=0
sina+cosa=0,
tana+1=0
tana=-1=k
ax+by+c=0
by=-ax-c
y=-ax/b-c/b
斜率k=-a/b=-1
a=b
a-b=0

sina+cosa=0
sina=-cosa
tana=-1
k=-1
因此-a/b=k=-1
即a-b=0

sina+cosa=0
sina=-cosa
tana=-1
ax+by+c=0
y=-a/bx-c/b
所以tana=-1=-a/b
a/b=1
a=b
a-b=0

sina=-cosa
tana=sina/cosa=-1
倾斜角的正切就是斜率
ax+by+c=0
y=(-a/b)x-c/b
斜率k=-a/b=-1
a=b
a-b=0