Let ABCDEFGHIJKL be a regular dodecagon. Then the value of `(AB)/(AF) + (AF)/(AB)` is equal to ____

Answer

4

Explanation

`AM = R sin.(pi)/(12) or AB sin.(pi)/(12)`
Similarly, `AN = R sin.(5pi)/(12) rArr AF = 2 R sin.(5pi)/(12)`

`:. (AB)/(AF) + (AF)/(AB) = (sin.(pi)/(12))/(sin.(5pi)/(12)) + (sin.(5pi)/(12))/(sin.(pi)/(12))`
`= tan.(pi)/(12) + cot.(pi)/(12)`
`= (2 - sqrt3) + (2 + sqrt3) = 4`