If cos 9α = sin α and 9α < 90° then the value of tan 5α is

$\cos 9 \alpha=\sin \alpha$

$\Rightarrow \cos 9 \alpha=\cos \left(90^{\circ}-\alpha\right)$

$\Rightarrow 9 \alpha=90^{\circ}-\alpha$

$\Rightarrow 10 \alpha=90^{\circ}$

$\Rightarrow 5 \alpha=\frac{90^{\circ}}{2}=45^{\circ}$

$\therefore \tan 5 \alpha=\tan 45^{\circ}=1$

Thus, the value of tan5α is 1.

Hence, the correct answer is option (c).