Sin 10° Sin 50° sin 70° = 1/8
Now we multiply upper & bottom both side 2/2
then
➡ 1/2 (2sin 10° sin50° 70°)
➡ 1/2 sin10°( 2sin70° sin50°)
we know that
2 sinA sinB = cos (A-B) - cos (A+B)
Then
➡ 1/2 sin 10° ( cos 20° - cos 120°)
➡ 1/2 sin 10° ( cos 20° - cos (90°+30°))
➡ 1/2 sin 10° ( cos 20° +1/2)
➡ 1/2 sin 10° cos 20° +1/4 sin 10°
again we multiply both upper & bottom side 2/2 so
➡ 1/4 ( 2 sin 10° cos 20°). + 1/4 sin 10°
we know that
2 sinA cos B = sin (A+B) - sin (A- B)
➡ 1/4 (sin 30° - sin 10°) + 1/4 sin 10°
➡ 1/4 sin 30° - 1/4 sin 10° + 1/4 sin 10°
we know sin 30° = 1/2
➡ 1/4 × 1/2
➡ = 1/8 hence proved