设cos（-80°）=k，那么tan100°=．

Question

设cos（-80°）=k，那么tan100°=______．

Answer 1

∵sin80°=√(1−cos280°)=√(1−cos2(−80°))=√(1−k2)，
所以tan100°=-tan80°=-(sin80°)/(cos80°)=-(sin80°)/(cos(−80°))=-(√(1−k2))/(k)．
故答案为：-(√(1−k2))/(k)．