  In this letter we show that the soft behaviour of photons and graviton
amplitudes, after projection, can be determined to infinite order in soft
expansion via ordinary on-shell gauge invariance. In particular, as one of the
particle's momenta becomes soft, gauge invariance relates the non-singular
diagrams of an n-point amplitude to that of the singular ones up to possible
homogeneous terms. We demonstrate that with a particular projection of the
soft-limit, the homogeneous terms do not contribute, and one arrives at an
infinite soft theorem. This reproduces the result recently derived from the
Ward identity of large gauge transformations. We also discuss the modification
of these soft theorems due to the presence of higher-dimensional operators.
