Question: syntax for is command

Am I applying improper syntax for the is command?  Out of the 5 attempts to equate X with the time derivative of S11 only the combine command yields the expected result.  If only combine works then why do the others not work?
 

Ck1 := sin(Pi*k)/(Pi*k); 1; Ck2 := (1-cos(Pi*k))/(Pi*k); 1; S11 := a[0]+int(sum(2*Ck2*Pi*k*cos(2*Pi*k*x/T)/T, k = 1 .. m), x = 0 .. t); -1; Q1 := 2*sin(alpha)*(diff(S11, t)); -1; Q3 := sum(2*Ck2*Pi*k*(sin(alpha+2*Pi*k*t/T)+sin(alpha-2*Pi*k*t/T))/T, k = 1 .. m); -1; is(Q1 = Q3)

true

(1)

sum1 := sum(2*Ck2*Pi*k*cos(2*Pi*k*x/T)/T, k = 1 .. m):

true

(2)

subs(x = t, simplify(expand(combine(2*sin(alpha)*sum1)))) = simplify(expand(combine(Q3)))"(->)"true

NULL

m := 2*n;

-4*sin(Pi*t/T)*sin(Pi*t*n/T)*cos(Pi*t*n/T)*(2*cos(Pi*t*n/T)^2-1)/(T*cos(Pi*t/T)*(-1+cos(Pi*t/T)^2))

(3)

is(`assuming`([X = diff(S11, t)], [n::integer])), is(`assuming`([expand(X = diff(S11, t))], [n::integer])), is(`assuming`([combine(X = diff(S11, t))], [n::integer])), is(`assuming`([eval(X = diff(S11, t))], [n::integer])), is(`assuming`([value(X = diff(S11, t))], [n::integer])), simplify(`assuming`([combine(X-(diff(S11, t)))], [n::integer]))

false, false, true, false, false, 0

(4)

X

-4*sin(Pi*t/T)*sin(Pi*t*n/T)*cos(Pi*t*n/T)*(2*cos(Pi*t*n/T)^2-1)/(T*cos(Pi*t/T)*(-1+cos(Pi*t/T)^2))

(5)

`assuming`([combine(X-(diff(S11, t)))], [n::integer])

0

(6)

`assuming`([X-combine(diff(S11, t))], [n::integer])

-4*sin(Pi*t/T)*sin(Pi*t*n/T)*cos(Pi*t*n/T)*(2*cos(Pi*t*n/T)^2-1)/(T*cos(Pi*t/T)*(-1+cos(Pi*t/T)^2))-(2*cos((-Pi*t+4*Pi*t*n)/T)-2*cos((Pi*t+4*Pi*t*n)/T))/(T*cos(Pi*t/T)-T*cos(3*Pi*t/T))

(7)

"(=)"

0

(8)

``


 

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