$4.75 \operatorname{ctg} 10^{\circ} \operatorname{ctg} 50^{\circ} \operatorname{ctg} 70^{\circ}=\operatorname{ctg} 30^{\circ}$.
4.75 In the left part of the supposed equality, we will proceed to the calculation of the numerator and the denominator. We have $\cos 10^{\circ} \cos 50^{\circ} \cos 70^{\circ}=\frac{1}{2}\left(\cos 60^{\circ}+\cos 40^{\circ}\right) \cos 70^{\circ}=$

$$
=\frac{1}{2}\left(\frac{1}{2} \cos 70^{\circ}+\frac{1}{2} \cos 110^{\circ}+\frac{1}{2} \cos 30^{\circ}\right)=\frac{1}{4} \cos 30^{\circ}
$$

## Similarly, we find

$\sin 10^{\circ} \sin 50^{\circ} \sin 70^{\circ}=\frac{1}{4} \sin 30^{\circ}$.

By dividing the first expression by the second, we get $\cot 30^{\circ}$.