The 1.0 coefficients can be changed to exact 1's in a variety of ways. A simple method is with Rationalize.
In[1]:= expr = (-0.5 Cos[1. (-3. + 1. a + 1. c - 1. d) pi] +
0.5 Cos[1. (-3. + 1. a - 1. c + 1. d) pi])/((-3. + 1. a) (c - 1. d) pi^2);
In[2]:= rexpr = Rationalize[expr]
-Cos[(-3 + a + c - d) pi] Cos[(-3 + a - c + d) pi]
------------------------- + ------------------------
2 2
Out[2]= ----------------------------------------------------
2
(-3 + a) (c - d) pi
In[3]:= Together[%]
-Cos[(-3 + a + c - d) pi] + Cos[(-3 + a - c + d) pi]
Out[3]= ----------------------------------------------------
2
2 (-3 + a) (c - d) pi
If by "pi", you mean 3.14159..., this can be simplified further.
In[4]:= FullSimplify[rexpr /. pi -> Pi, Element[{a, c, d}, Reals] ]
Sin[a Pi] Sin[(c - d) Pi]
Out[4]= -(-------------------------)
2
(-3 + a) (c - d) Pi
where
In[5]:= ? /.
expr /.rules applies a rule or list of rules in an attempt to transform each subpart of
an expression expr.
In[6]:= ? ->
lhs -> rhs represents a rule that transforms lhs to rhs.
