若直线L1 的斜率为K1,倾斜角为a1,直线 L2的斜率为K2,倾斜角为a2,且a1+a2=90度,则k1+k2的最小值

k1+k2=tana1+tan(90-a1)
=sina1/cosa1+sin(90-a1)/cos(90-a1)
=[sina1cos(90-a1)+cosa1(90-a1)]/cosa1cos(90-a1)
=sin(a1+90-a1)/{[sin(a1+90-a1)-sin(a1-90+a1)]/2}
=2sin90/[sin90-sin(2a1-90)]
=2/[1+sin(90-2a1)]
=2/(1+cos2a1)
因为倾斜角大于等于0,小于180度
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