b)VT= $tan30^0+tan40^0+tan50^0+tan60^0$
= $tan30^0+cot30^0+tan40^0+cot40^0$
= $\frac{1}{sin30^0.cos30^0}+\frac{1}{sin40^0.cos40^0}$
= $\frac{2}{sin60^0}+\frac{2}{sin80^0}$
= $\frac{2(sin80^0+sin60^0)}{sin80^0.sin60^0}$
= $\frac{4}{\sqrt{3}}.\frac{2.sin70^0.cos10^0}{sin80^0}$
= $\frac{8}{\sqrt{3}}.cos20^0.\frac{cos10^0}{cos10^0}$
=$\frac{8\sqrt{3}}{3}.cos20^0$
= VP (dpcm)