The value of cos ⁡ π 11 cos ⁡ 2 π 11 cos ⁡ 3 π 11 … … cos ⁡ 11 π 11 is equal to

Step-by-step solution

Required expression = cos ⁡ π 11 cos ⁡ 2 π 11 cos ⁡ 3 π 11 cos ⁡ 4 π 11 cos ⁡ 5 π 11 2 = cos ⁡ π 11 cos ⁡ 2 π 11 cos ⁡ 8 π 11 cos ⁡ 4 π 11 cos ⁡ 5 π 11 2 = sin ⁡ 16 π 11 16 sin ⁡ π 11 × cos ⁡ 5 π 11 2 = 2 sin ⁡ 5 π 11 cos ⁡ 5 π 11 32 sin ⁡ π 11 2 = sin ⁡ 10 π 11 32 × sin ⁡ π 11 2 = 1 32 2 = 1 1024