tan10xtan20+tan20xtan60+tan60xtan10的值是多少
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tan10xtan20+tan20xtan60+tan60xtan10的值是多少
tan10xtan20+tan20xtan60+tan60xtan10的值是多少
tan10xtan20+tan20xtan60+tan60xtan10的值是多少
tan60=根号3
tan30=根号3/3
tan(α+β)=(tanα+tanβ)/(1-tanα·tanβ)
tan(10+20)=(tan10+tan20)/(1-tan10tan20)
(tan10+tan20)=tan30*(1-tan10tan20)
原式=tan10xtan20+(tan20+tan10)*tan60
=tan10xtan20+(1-tan10tan20)
=1