What is the value of sin10°·sin50° + sin50°·sin250° + sin250°·sin10° equal to?
A.–1/4
B.–3/4✓ Correct
C.3sin10°/4
D.–3cos10°/4
Explanation
Note sin250° = sin(180°+70°) = –sin70° = –cos20°. Also sin50° = cos40°. The identity sin A sin B + sin B sin C + sin C sin A where A, B, C are at 120° intervals equals –3/4. Here 10°, 50°, 250° differ as 50°–10°=40°, 250°–50°=200°, etc. Actually 10°, 130°, 250° are 120° apart. sin130° = sin50°. So sin10°, sin130°, sin250° are sines of angles 120° apart, and sin10°·sin130° + sin130°·sin250° + sin250°·sin10° = –3/4 (standard identity).
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