I will reiterate:
I am not sure if I should place this posting here or in my other questions of sum vs add or sum vs Sum. I will try here 1st. My results in the link below show concurrence between add & sum commands (see result (8)), and the difference in their computation demands. In this posting we circumvent the computation demands of sum via use of Sum & add.with a trick presented by @acer. Unfortunately, after appying this trick the concurrence between add& sum does not seem to be valid any longer (see result (11)). Result (12) shows that they are nearly identical numerically. Why are they no longer EXACTLY identical? My guess is the application of the integral in S1. However, result (13) shows the integral relation between the sin(x) & cos(x) which is EXACT.
Am I expecting too much from MAPLE? I have always had the impression that MAPLE is quite superior at handling these identities so I would expect concurrence between S9 & test. Perhaps I am bucking against the INERT vs ACTIVE commands once again?
See my latest results as posted on:
If MAPLE cannont recognize this I think evaluating it numerically maybe can be sufficient, but that does NOT satisfy the 2 expressions are UNIVERSALLY equivalent which they are. Numerical evaluation might support local approximation of a nonlinear function, but does not show GLOBAL or UNIVERSAL equivalence. So the fact that MAPLE crashes seems to suggest it is attempting to evaluate the difference & does not recognize the difference should be =0.