Because over the interval [0,pi] the functions sin(nx), n=1, 2, .. are

orthogonal, and so the coefficients of multiples of sin(nx) on one side must

be the same as those on the other of such an equation (with a few

assumptions about the nature of the T's anyway - such as the T's and

their second derivatives are integrable on [0,pi], and that we are only interested

in their values on [0,pi] or they are odd priodic functions of period 2pi )

RonL