  For the group G=PGL_2 we perform a comparison between two relative trace
formulas: on one hand, the relative trace formula of Jacquet for the quotient
T\backslash G/T, where T is a non-trivial torus, and on the other the Kuznetsov
trace formula (involving Whittaker periods), applied to non-standard test
functions. This gives a new proof of the celebrated result of Waldspurger on
toric periods, and suggests a new way of comparing trace formulas, with some
analogies to Langlands' "Beyond Endoscopy" program.
