Question

In \( \triangle ABC \), \( \angle C = 90^\circ \), then \( \sin(A + B) = \)

• A. 0
• B. 1
• C. \( \frac{1}{2} \)
• D. \( \frac{1}{\sqrt{2}} \)

Hint:

In any right triangle, the sum of the two non-right angles is \( 90^\circ \), leading to \( \sin(A + B) = 1 \).

Answer 1

The Correct Option is B

Step 1: In a right triangle, the sum of the angles is \( 180^\circ \), and since \( \angle C = 90^\circ \), we have: \[ A + B = 90^\circ \] Step 2: Using the identity \( \sin(90^\circ) = 1 \), we get: \[ \sin(A + B) = \sin 90^\circ = 1 \] Thus, the correct answer is \( \boxed{1} \).