Ali is studying a certain signal that they processed using old software. This software outputs a model for the derivative of as 2t 5 2mt 5 (1) = 5 cos23 (WT) sin\"" (WT), where > 0, for some positive integer m. However, the software is not designed to find a formula for ( itself, so Ali decides to tediously calculate this by hand. (a) By using a certain formula, Ali is able to expand /(p"(t) dt into a sum of terms of the form 2wt 5\\ . pf27t5 A[COS(T) sin (T) dt, for some A R and for certain integers k N. Assuming they've done everything correctly, how many terms like this will there be in Ali's expansion of f up"(t) dt? The number of terms will be 12 B (b) Geonwoo is working at the same time on the same problem, but obtains a different (but still correct) expansion. For example, the 7th term in Geonwoo's expansion (without the coefficient) is Iz = /coss (#) sinldtm (#) dt. Assuming that the constant of integration is zero, Geonwoo then used Ali's procedure from part (a) to calculate [ 7 in the form 2wt 5 2mt 5 In = sin\" (T) + sin'r"'z (T) , forsomea,pB,veR. If Geonwoo has also done everything correctly, what are , 3 and -y above? Syntax advice: Enter your answer using Maple notation with * for mulitplication, Pi for and don't forget to use 7+m brackets to group terms in a numerator or denominator of a fraction. For example, for ~ you would enter 2k (7+Pi) / (2*k). a= & [ B B [ Y= &amp