Question

cos(π/11).cos(2π/11).cos(3π/11).cos(4π/11).cos(5π/11)=1/32

Answer 1

This is very lengthy answer . So I will solve this without showing formulas.

Multiply and divide with 2sin π/11

2(sinπ/11 ×cosπ/11) ×cos2π/11 ......Cos 5π/11/2sin π/11

2(sin 2 π/11 × cos 2π/11) cos3π/11....cos5π/11/4sinπ/11

2 (sin4π/11×cos 4π/11) cos 3π/11 cos 5π/11. /8 sinπ/11

2(sin3π/11×cos3π/11) cos5π/11 / 16sin π/11

Cos 5π/11 = cos -6π/11

-2 (sin 6π/11 × cos 6π/11) / 32 sin π/11

-sin12π/11 / 32 sin π/11

Sin π/11 / 32sin π/11 = 1/32