(7) $\cos \left(\sqrt{1-\sqrt{x^{2}+5 x+7}}+\sqrt{x^{2}+5 x+6}\right)=$
According to the problem,
$$
\begin{array}{c}
x^{2}+5 x+6 \geqslant 0, \\
0 \leqslant x^{2}+5 x+7 \leqslant 1 .
\end{array}
$$

Therefore,
$$
x^{2}+5 x+7=1 .
$$

Thus,
$$
\cos \left(\sqrt{1-\sqrt{x^{2}+5 x+7}}+\sqrt{x^{2}+5 x+6}\right)=\cos 0=1 .
$$