  Let $G$ denote a distance-regular graph with diameter $D\ge 3$, valency $k$,
and intersection numbers $a_i$, $b_i$, $c_i$. By a {\it pseudo cosine sequence}
of $G$ we mean a sequence of real numbers $s_0, s_1, ..., s_D$ such that
$s_0=1$ and $c_i s_{i-1}+a_i s_i+b_i s_{i+1}=k s_1 s_i$ for $ 0 \le i \le D-1$.
Let $s_0, s_1,..., s_D$ and $p_0, p_1, ..., p_D$ denote pseudo cosine sequences
of $G$. We say this pair of sequences is {\it tight} whenever $s_0 p_0, s_1
p_1, ..., s_D p_D$ is a pseudo cosine sequence of $G$. In this paper, we
determine all the tight pairs of pseudo cosine sequences of $G$.
