What is \cos^{2}A+\cos^{2}B+\cos^{2}C equal to?
A triangle ABC with sides AB=15\text{ cm}, BC=9\text{ cm}, CA=12\text{ cm} is inscribed in a circle.
- A. \frac{3}{4}
- B. 1 ✓
- C. \frac{5}{4}
- D. 2
Correct Answer: B. 1
Explanation
The sides 9, 12, 15 form a right-angled triangle (9^2 + 12^2 = 15^2), with \angle C = 90^\circ. Therefore, \cos C = 0, and angles A and B are complementary. Thus, \cos B = \sin A. The expression becomes \cos^2 A + \sin^2 A + 0 = 1.
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