因为tan100°=m,所以平方得：（tan100°）^2=m^2,即：(sin100°)^2/(cos100°)^2=m^2
则：[1-(cos100°)^2]/(cos100°)^2=m^2
(cos100°)^2=1/(m^2+1)
cos100°=-1/根号(m^2+1).