The value of (2 tan 24°)/(cot 66°) + (cot 37°)/(tan 53°) is:

\(\frac{2 tan 24°}{cot 66°}\) + \(\frac{cot 37°}{tan 53°}\)

= 2 + 1 = 3

(because if A + B = 90°, then \(\frac{tan A}{tan B}\) = 1)