reserve q,th,r for Real,
  a,b,p for Real,
  w,z for Complex,
  k,l,m,n,n1,n2 for Nat,
  seq,seq1,seq2,cq1 for Complex_Sequence,
  rseq,rseq1,rseq2 for Real_Sequence,
  rr for set,
  hy1 for 0-convergent non-zero Real_Sequence;
reserve d for Real;
reserve th,th1,th2 for Real;

theorem Th36:
  cos.th=Sum(th P_cos) & sin.th=Sum(th P_sin)
proof
  reconsider th as Real;
   sin.th = Im(Sum((th*<i>) ExpSeq)) & cos.th=Re(Sum((th*<i>) ExpSeq)) by Def16
,Def18;
  hence thesis by Th35;
end;
