If `DeltaABC` is right angle at C, then value of cos (A+B) is:

Options

A. 0
B. 1
C. `1/2`
D. `sqrt3/2`

Answer

To solve the problem, we need to find the value of cos(A + B) given that triangle ABC is a right triangle with the right angle at C.

### Step-by-Step Solution:

1. **Understanding the Triangle**: In triangle ABC, we know that angle C is 90 degrees. Therefore, we can write:
\[ A + B + C = 180^\circ \]

2. **Substituting the Value of C**: Since C is 90 degrees, we can substitute this into the equation:
\[ A + B + 90^\circ = 180^\circ \]

3. **Solving for A + B**: Rearranging the equation gives us:
\[ A + B = 180^\circ - 90^\circ \]
\[ A + B = 90^\circ \]

4. **Finding cos(A + B)**: Now that we know A + B = 90 degrees, we can find cos(A + B):
\[ \cos(A + B) = \cos(90^\circ) \]

5. **Using the Value of cos(90°)**: We know from trigonometric values that:
\[ \cos(90^\circ) = 0 \]

6. **Final Answer**: Therefore, the value of cos(A + B) is:
\[ \cos(A + B) = 0 \]

### Summary:
The value of cos(A + B) when triangle ABC is a right triangle at C is 0.