Calculate :
Outline solution: For x = 1,2,3,...,90, (where x is measured in degrees). The formula for is of the form . The part in parentheses is a polynomial of degree 178 in , with all but the first and last terms omitted.
If we put that expression equal to 0 then the factor corresponds to x=90 and x=–90, and the factor corresponds to x=0. If we write s for then the 178 roots of the polynomial are for . But the product of the roots of a polynomial of even degree is the constant term divided by the coefficient of the leading term. Therefore , and hence (and of course , so that does not contribute to the product).