The value of sin ⁡ 9 π 14 sin ⁡ 11 π 14 sin ⁡ 13 π 14 is equal to

Step-by-step solution

sin ⁡ 9 π 14 sin ⁡ 11 π 14 sin ⁡ 13 π 14 = sin ⁡ π 2 + π 7 sin ⁡ π 2 + 2 π 7 sin ⁡ π 2 + 3 π 7 = cos ⁡ π 7 cos ⁡ 2 π 7 cos ⁡ 3 π 7 = cos ⁡ π 7 cos ⁡ 2 π 7 cos ⁡ π - 4 π 7 = - cos ⁡ π 7 cos ⁡ 2 π 7 cos ⁡ 4 π 7 = - sin ⁡ 8 π 7 8 sin ⁡ π 7 = - sin ⁡ π + π 7 8 sin ⁡ π 7 = 1 8