NDA 2024 · PYQ · Trigonometry / Triangles · medium
In triangle ABC, AB = 16 cm, BC = 63 cm and AC = 65 cm. What is cos2A + cos2B + cos2C?
A.–1✓ Correct
B.0
C.1
D.76/65
Explanation
Check if right-angled: 16² + 63² = 256 + 3969 = 4225 = 65². So triangle is right-angled at B (since AC is hypotenuse), making angle B = 90°. For any triangle, cos2A + cos2B + cos2C = –1 – 4cosA cosB cosC. With B = 90°, cosB = 0, so cos2A + cos2B + cos2C = –1.
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