Question

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

Options

• 0

• 1

• `1/2`

• `sqrt(3)/2`

Answer 1

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