Without using calculator or mathematical table, simplify 2tan60° + cos30°÷ sin60°

Answer 1

You should memorize the ratio of sides of the standard 30-60-90 rightangled triangle. I would add to that the 45-45-90 triangle.
2tan60° + cos30°/sin60°
= 2√3 +(√3/2) / (√3/2)
= 2√3 + 1