Question

Prove that: sin 70° - sin 50° = sin 10°​

Answer 1

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