How to make mathematica gives the imaginary part of a certain complex function in the form of trigonometric functions such as sin(s-t) and cos(s-t)?
Clear["Global`*"]; et[s_] := Cos[s] + I Sin[s]; etp[s_] := I et[s]; A[s_] := (et[s])^3; NM[s_, t_] := Im[A[s]/A[t] etp[t]/(et[t] - et[s])];
From the coding, I only manage to get answer
Re[(Cos[s] + I Sin[s])^3/((Cos[t] + I Sin[t])^2 (-Cos[s] + Cos[t] - I Sin[s] + I Sin[t]))]
which is not real expression because still have
I. I don't understand why the
Im doesn't work. Later on I have more complicated function
et[s_]:=(3+2 Cos[2s])(Cos[s] + I Sin[s])