## [Hints] 2014 Singapore MO (Open Rd 1) Problem 16

2014 SMO (Open-Rd1) 16. Let $ABC$ be a triangle with $a = BC$, $b = AC$, and $c = AB$. Assume that $3a^2 + 3b^2 = 5c^2$. Find the value of

$\displaystyle\frac{\cot A + \cot B}{\cot C}.$

Hint 1: Express the fraction in terms of sines and cosines. What formulas can we apply after that?

Hint 2: Sine rule, followed by Cosine rule.