Question

If $∆ABC$ is right angled at C , then the value of cos ( $A+B$ ) is

Answer 1

In a right angled triangle ABC, $\angle \mathrm{C}$ is a right angle.
We know that, the sum of angles of a triangle is 180º.
$$\begin{gathered} \therefore \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180° \\ \Rightarrow \angle \mathrm{A}+\angle \mathrm{B}+90°=180° \\ \Rightarrow \angle \mathrm{A}+\angle \mathrm{B}=90° \end{gathered}$$
$\therefore \cos \left(\mathrm{A}+\mathrm{B}\right)=\cos 90°=0$
Hence, the correct answer is option (a).