ABC is a triangle inscribed in a semicircle of diameter AB. What is \cos(A+B) + \sin(A+B) equal to?
- A. 0
- B. \frac{1}{4}
- C. \frac{1}{2}
- D. 1 ✓
Correct Answer: D. 1
Explanation
The angle subtended by a diameter at the circumference is always a right angle, so \angle C = 90^\circ. By angle sum property, A + B = 90^\circ. Therefore, \cos(90^\circ) + \sin(90^\circ) = 0 + 1 = 1.
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