Proof. Introducing the substitution 8 arccos(a) changes this equation to Tn(B(a )=Tm(0)=cos(n0), where 8E[0, T) A recurrence relation is derived by noting that Tn+1(0)=cos(ne)cos(0)-sin(ne )sin() ant T-1(0)=cos(ne)cos(0)+sin(ne)sin(g) O Tn+1(6)=2c0s(n6)cos()-Tn-1(6) Returning to the variable a gives Tn+1(a)=2 Tn()-Tn-1(a), for each n21