Understanding the Triangle ABC
In triangle ABC, where the angle C is the right angle, we can analyze the angles A and B. By the properties of triangles, we know that:
- The sum of angles in a triangle is 180 degrees.
- Since angle C is 90 degrees, angles A and B must sum up to 90 degrees.
Relationship between Angles A and B
- Therefore, we can express this relationship as: A + B = 90 degrees.
Calculating cos(A + B)
- Now, we need to find cos(A + B). Since we established that A + B = 90 degrees, we can rewrite this as:
cos(A + B) = cos(90 degrees)
Value of cos(90 degrees)
- The value of cos(90 degrees) is well-known in trigonometry:
- cos(90 degrees) = 0
Conclusion
- Hence, for triangle ABC right-angled at C, the value of cos(A + B) is:
- cos(A + B) = 0
This result highlights the unique properties of right-angled triangles and the fundamental relationships between the angles. Remember these relationships as they form the basis for understanding trigonometric concepts further!