∏ j = m n cos ( 2 j θ ) = 2 n − m + 1 s i n ( 2 m θ ) s i n ( 2 n + 1 θ ) whenever the denominator is nonzero. Evaluate ∏ j = 1 11 cos ( jπ /11 ) .

Question

∏ j = m n ​ cos ( 2 j θ ) = 2 n − m + 1 s i n ( 2 m θ ) s i n ( 2 n + 1 θ ) ​ whenever the denominator is nonzero. Evaluate ∏ j = 1 11 ​ cos ( jπ /11 ) .

TestHub · Accepted Answer

Pair terms at angles jπ/11 and (11 - j)π/11, then include cos π = -1: the product equals (∏(j=1 to 5) cos(jπ/11))². The standard odd-angle product is ∏(j=1 to 5) cos(jπ/11) = 1/32, so the answer is 1/1024.

Mathematics - Trigonometric Equation Question with Solution | TestHub

Options:

Doubts & Discussion