Question

If in ΔABC, ∠C = 90°. Then, the value of cos(A + B) is

(a) 0

(b) 1

(c) $\frac{1}{2}$

(d) $\frac{3}{5}$

Answer 1

In ∆ABC,

∠A + ∠B + ∠C = 180º (Angle sum property of triangle)

⇒ ∠A + ∠B + 90º = 180º (∠C = 90º)

⇒ ∠A + ∠B = 180º − 90º = 90º

∴ cos(A + B) = cos90º = 0

Thus, the value of cos(A + B) is 0.

Hence, the correct answer is option (a).