theorem Th25: :: TAYLOR_2:25

for r, x being Real
for m being Nat st 0 < r holds
( (Partial_Sums (Maclaurin (sin,].(- r),r.[,x))) . ((2 * m) + 1) = (Partial_Sums (x P_sin)) . m & (Partial_Sums (Maclaurin (cos,].(- r),r.[,x))) . ((2 * m) + 1) = (Partial_Sums (x P_cos)) . m )