解：∵tan(x+y)=(tanx+tany)/(1-tanxtany)
tanx+tany=tan(x+y)*(1-tanxtany)
tan(90-x)=sin(90-x)/cos(90-x)=cosx/sinx=1/tanx
原式=tan10*(tan20+tan60)+tan20*tan60
=tan10*tan80*(1-tan20tan60)+tan20tan60
=1-tan20tan60+tan20tan60
=1
答：原式=1
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