If Cot \(x = \frac{5}{12},\) then Sin \(x + \frac{1}{Cot \ x} + sec \ x \ = \ ?\)

cot x = 5/12 gives a 5–12–13 triangle: sin x = 12/13, tan x = 1/cot x = 12/5 and sec x = 13/5. Sum = 12/13 + 12/5 + 13/5 = 12/13 + 5 = 77/13.