Infinitely many solutions

Preben Alsholm — Sun, 06 Jan 2013 20:44:44 Z

There are infinitely many solutions.

For each constant a<>0 the function

f:=x->sin(Pi/2/a*x);
#is a solution:
expand(f(x+y));
simplify(f(x)*f(a-y)+f(y)*f(a-x));
f(2013^(1/2013));

(These solutions were just found from recalling the well known addition formula for the sine function).

And by the way: By observation the constant function f(x) = 1/2 is a solution too (besides the trivial solution f(x)=0).

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