Introduction to Trigonometry
RD Sharma
CBSE
Grade 10
Question:
If $\Delta ABC$ is right-angled at $C$, then the value of $\cos(A + B)$ is:
(a) $0$
(b) $1$
(c) $\dfrac{1}{2}$
(d) $\dfrac{\sqrt{3}}{2}$
Step-by-Step Solution
Key Concept: In $\Delta ABC$, $\angle C = 90^\circ \Rightarrow A + B = 90^\circ \Rightarrow \cos(A + B) = \cos 90^\circ = 0$.
$A + B + C = 180^\circ \Rightarrow A + B = 90^\circ \Rightarrow \cos(90^\circ) = 0$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating $\cos 90^\circ = 0$: 1.0 Mark
Correct Answer: $0$
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