Question

Tg30*×ctg60*+tg60*×ctg30*= 10 supra 3

Answer 1

[tex]\it tg30^o=ctg60^o=\dfrac{\sqrt3}{3} \\ \\ tg60^o=ctg30^o=\sqrt3 \\ \\ tg30^o\cdotctg60^o +tg60^o\cdotctg30^o=\dfrac{\sqrt3}{3}\cdot\dfrac{\sqrt3}{3}+\sqrt3\cdot\sqrt3=\dfrac{3}{3\cdot3}+3= \\ \\ =\dfrac{1}{3} +3= 3+\dfrac{1}{3}=\dfrac{10}{3}[/tex]