Question

If in \( \triangle ABC \), \( \angle C = 90^\circ \), then \( \sin(A + B) \) is:

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

Hint:

In a right-angled triangle, the sum of the other two angles is always \( 90^\circ \).

Answer 1

The Correct Option is B

In any triangle:
\[ A + B + C = 180^\circ \] Since \( C = 90^\circ \):
\[ A + B = 90^\circ \] Thus:
\[ \sin (A + B) = \sin 90^\circ = 1 \]