# Trigonometry inequality problem

If $\lvert \cos A \cos B \cos C\rvert =\frac{2}{3}$, then find the maximum value of $\tan A \tan B + \tan B\tan C + \tan C\tan A$

I have no idea how to approach this question. I tried converting all tans to sin and cos, but that didn't help in any way. Then I thought maybe complex numbers will be used, but I wasn't able to understand how!

• What are $A,B,C$, triangle angles? – Dr. Sonnhard Graubner Apr 21 '18 at 9:56
• It isn't mentioned anywhere, I first of thought of that only seeing the general A, B, C angles, but it isn't mentioned. – Avinash Bhawnani Apr 21 '18 at 9:58

## 1 Answer

Ahh, expansion of cos(a+b+c) will do it.