The formula given, \( \cos(a+b) = \cos(a) \cos(b) - \sin(a) \sin(b) \), is known as the cosine addition formula.

The question appears to ask for a proof or verification of certain identities involving angles A, B, and C in a triangle. The specific context seems to involve proving a relationship regarding the tangent function.

To summarize some key aspects based on the image:

1. **Tangent Addition Formula**:
\[
\tan(a+b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}
\]

2. **For angles in a triangle**:
You may need to show that the tangent of the sum of two angles relates to their individual tangents.

3. **Given conditions**: It notes - for triangle ABC (not a right triangle), possibly with additional conditions or values needed to find specific tangents or relations.

If you need a specific proof or further computations, please provide additional details!