The form of teeth formed based on Tredgold's Approximation depends upon the slant height of the back cone (not on the radius R). A sphere is approximated between the back cone and pitch cone as shown in the figure below. The back cone is forming the teeth of the equivalent spur gear. Thus, the equivalent pitch radius of the back cone is $R_{e}=R / \cos \Gamma \quad \text{OR} \quad R_{e}=R / \cos \delta$ (In PSG pitch cone angle is denoted by $\delta$).

Hence equivalent number of teeth on spur gear is $Z_{e}=\frac{p c d}{m o d u l e}=\frac{2 R_{e}}{m}=\frac{2 R}{m \cos \Gamma}= \left(\frac{2 R}{m}\right) \frac{1}{\cos \Gamma}=\frac{Z}{\cos \Gamma}$ or $\frac{Z}{\cos \delta}$

The action of the bevel gears will be the same as that of the equivalent spur gears. Since the equivalent number of teeth is always greater than the actual number of teeth, a given pair of bevel gears will have a larger contact ratio and will run more smoothly than a pair of spur gears with the same number of teeth.