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

Question

The value of cos &#8289; &#960; 2 2 &#8901; cos &#8289; &#960; 2 3 &#8901; &#8230; &#8901; cos &#8289; &#960; 2 10 &#8901; sin &#8289; &#960; 2 10 is:

Aicharya · Accepted Answer

Given c o s &#960; 2 2 &#183; c o s &#960; 2 3 &#183; . . . &#183; c o s &#960; 2 10 &#183; s i n &#960; 2 10 = sin 2 9 . &#960; 2 10 2 9 . sin &#960; 2 10 . sin &#960; 2 10 Using &#160; &#160; 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

The value of cos ⁡ π 2 2 ⋅ cos ⁡ π 2 3 ⋅ … ⋅ cos ⁡ &#960…

Solution

The value of cos &#8289; &#960; 2 2 &#8901; cos &#8289; &#960; 2 3 &#8901; &#8230; &#8901; cos &#8289; &#960…

Solution

The value of cos ⁡ π 2 2 ⋅ cos ⁡ π 2 3 ⋅ … ⋅ cos ⁡ &#960…