### If $\triangle ABC$ is right angled at $C$, find the value of $cos(A+B)$.

$0$

Step by Step Explanation:
1. We know that sum of the angles of a triangle is $180^\circ$
$\angle A + \angle B + \angle C = 180^\circ$
2. It is given that angle $C$ is right angle. Replace $\angle C = 90^\circ$ in above equation
$\implies \angle A + \angle B + 90^\circ = 180^\circ$
$\implies \angle A + \angle B = 180^\circ - 90^\circ$
$\implies \angle A + \angle B = 90^\circ$
3. Now we know the value of $A + B$, we can find the value of $cos(A+B)$
$\implies cos(A+B) = cos(90^\circ)$
$\implies cos(A+B) = 0$