[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.

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