Matematické Fórum

Skrytý text:
Let us prove that



Firstly we divide the product into two expresions. In the second one, we use the identity and put both products together. 



Next we use two results of complex analysis - exponential form of a complex number and a special identity for an imaginary part of a complex nubmer, i.e.



We get that



Now let us focus on the expression with which is closely related to roots of the binomial equation . All the complex roots of the equation can be written just in the form with and therefore the following identities hold true



The product of our interest can be simplified as follows



and we deduce that



Since all the sine functions in the product are positive, we can finally write that .