In a right triangle, if $\sin\theta = \frac{a}{b}$ and $\tan\theta = \frac{a}{c}$, identify the sides:

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{b} \implies \text{opposite} = a, \; \text{hypotenuse} = b$

$\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{c} \implies \text{adjacent} = c$

Therefore:

$\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{c}{b}$