1.

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

Answer»


Solution :`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`


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