The value of cos ⁡ π 2 2 ⋅ cos ⁡ π 2 3 ⋅ … ⋅ cos ⁡ π 2 10 ⋅ sin ⁡ π 2 10 is:

Step-by-step solution

Given c o s π 2 2 · c o s π 2 3 · . . . · c o s π 2 10 · s i n π 2 10 = sin 2 9 . π 2 10 2 9 . sin π 2 10 . sin π 2 10 Using cos A . cos 2 A . cos 2 2 A . cos 2 3 A . cos 2 4 A . . . . . cos 2 n - 1 A = sin 2 n A 2 n sin A = 1 2 9 = 1 512