Question

Sin70° sin130° sin170°=1/8​

Answer 1

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