Solving Acute Triangle Angles Given $A,B,C$ & Equations

[maxkor]

Given that $A,B,C$ be angles in an acute triangle.

If $(5+4\cos A)(5-4\cos B)=9$ and $(13-12\cos B)(13-12\cos C)=25$

find $cos(A+C)$.
I know $A+B+C=180^{o}$ and $\cos B=-\cos(A+C)$ and what next?

 

[lfdahl]

Hi, maxkor!(Wave)

Thankyou for sharing your problem on the MHB site!

You ask for the next step. One way (which worked for me) would be to isolate $\cos B$ in both equations.

I suggest, you try this out(Nod)