Question

# If $$\triangle ABC$$ is a right angled triangle, right angled at C, then $$\cos (A + B) =$$

A
0
B
12
C
1
D
32

Solution

## The correct option is D $$0$$Given that $$\triangle ABC$$ is a right angled triangle, with $$\angle C=90^o$$To find out: The value of $$\cos(A+B)$$In $$\triangle ABC$$,$$\angle A+\angle B+\angle C=180^o\quad \quad [\text{Angle sum property}]$$$$\Rightarrow \angle A+\angle B+90^o=180^o$$$$\Rightarrow \angle A+\angle B=180^o-90^o$$$$\therefore \ \angle A+\angle B=90^o$$Now, $$\cos(A+B)=\cos90^o$$We know that, $$\cos 90^o=0$$$$\therefore \ \cos(A+B)=0$$Hence, the required value of $$\cos(A+B)$$ for the given triangle is $$0$$.Mathematics

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