$ABC$ is a triangle such that angle $C = 60^{\circ}$, then what is $\frac{\cos A + \cos B}{\cos \left(\frac{A - B}{2}\right)}$ equal to?

In a triangle $ABC$, $AB=16 \text{ cm}, BC=63 \text{ cm}$ and $AC=65 \text{ cm}$. What is the value of $\cos 2A+\cos 2B+\cos 2C$?

Consider the following statements:

1. In a triangle $ABC$, if $\cot A \cdot \cot B \cdot \cot C>0$, then the triangle is an acute-angled triangle.

2. In a triangle $ABC$, if $\tan A \cdot \tan B \cdot \tan C > 0$, then the triangle is an obtuse-angled triangle.

Which of the statements given above is/are correct?

Consider the following for the next items that follow:

The angles A, B and C of a triangle ABC are in the ratio 3 ∶ 5 ∶ 4.