FLMPotD
Show that the ring Q[sin,cos] (say as a subring of the ring of functions on R) is spanned by the functions sin nx and cos nx as n varies.
(This one's from somthng2remembr. There's an unenlightening trivial solution using obscure trig identities, and then a more interesting conceptual solution.)
(This one's from somthng2remembr. There's an unenlightening trivial solution using obscure trig identities, and then a more interesting conceptual solution.)