96 cos π 33 cos 2 π 33 cos 4 π 33 cos 8 π 33 cos 16 π 33 is equal to

Step-by-step solution

Given, Expression 96 · cos π 33 · cos 2 π 33 · cos 4 π 33 . . . . . . . . . cos 16 π 33 Now we know that, cos A · cos 2 A · cos 2 2 A · cos 2 3 A . . . . . · cos 2 n - 1 A = sin 2 n A 2 n sin A Now using the above formula in given expression we get, 96 · cos π 33 · cos 2 π 33 · cos 4 π 33 . . . . . . . . . cos 16 π 33 = 96 × sin 32 π 33 2 5 sin π 33 = 96 × sin π - π 33 2 5 sin π 33 = 96 &#215