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Question
If ∆ABC is right angled at C, then the value of cos (A + B) is ______.
Options
0
1
`1/2`
`sqrt(3)/2`
Solution
If ∆ABC is right angled at C, then the value of cos (A + B) is 0.
Explanation:
We know that,
In ∆ABC,
Sum of three angles = 180°
i.e., ∠A + ∠B + ∠C = 180°
But right angled at C
i.e., ∠C = 90° ...[Given]
∠A + ∠B + 90° = 180°
⇒ A + B = 90° ...[∵∠A = A]
∴ cos (A + B) = cos 90° = 0
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