Prove that: sin10° sin30° sin50° sin70° = 1/16
Prove that sin 10° sin 30° sin 50° sin 70° = 1/16
L.H.S. = sin 10° sin 30° sin 50° sin 70°
= 1/2 (sin 10° sin 50°) sin 70° (sin 30° = 1/2)
= 1/4 (2 sin 10° sin 50°) sin 70°
= 1/4 [cos 40° - cos 60°] sin 70°
= 1/4 [cos 70° - cos 40° - 1/2 sin 70°]
= 1/8 [2 sin 70° cos 40° - sin 70°]
= 1/8 [sin 110° + sin 30° - sin 70°]
= 1/8 [sin (180° - 70°) + sin 30° - sin 70°]
= 1/8 [sin 70° + 1/2 - sin 70°]
= 1/16R.H.S.