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Step-by-step explanation:
sin α - sin β = 2 cos (α + β)/2 sin (α - β)/2
sin 70° - sin 50° = sin 10°
2 cos (70° + 50°)/2 sin (70° - 50°)/2 = sin 10°
2 cos 120°/2 sin 20°/2 = sin 10°
2 cos 60° sin 10° = sin 10°
2 (½) sin 10° = sin 10°
sin 10° = sin 10° → Proved