myrules={Cos[a_]Cos[b_]->(Cos[a+b]+Cos[a-b])/2,​​Cos[a_]^2->(1+Cos[2*a])/2,c_->Expand[c]};​​k[0,t_]=1;​​k[n_,t_]=Cos[t]*k[n-1,t]+Cos[n*t]//.myrules;​​Table[k[n,t],{n,0,2}]//TableForm
$RecursionLimit
:Recursion depth of 1024 exceeded.
Out[]//TableForm=
1
Cos[t]+Cos[t]TerminatedEvaluation[RecursionLimit]
Cos[2t]+Cos[t]TerminatedEvaluation[RecursionLimit]
Set
:Cannot assign to raw object 3.
​