√3tan21°*tan39°+tan21°+tan39°=

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√3tan21°*tan39°+tan21°+tan39°=
√3tan21°*tan39°+tan21°+tan39°=

√3tan21°*tan39°+tan21°+tan39°=
tan(a+b)=(tanA+tanB)/(1-tanAtanB)
(1-tanAtanB)=(tanA+tanB)/tan(A+B)
tanAtanB)=1-(tanA+tanB)/tan(A+B)
√3tan21°*tan39°+tan21°+tan39°
=√3[1-(tan21°+tan39°)/tan(21°+39°)]+tan21°+tan39°
=√3-√3(tan21°+tan39°)/tan(60°)+tan21°+tan39°
=√3-√3(tan21°+tan39°)/√3+tan21°+tan39°
=√3-(tan21°+tan39°)+tan21°+tan39°
=√3-tan21°-tan39°+tan21°+tan39°
=√3