In Doppler effect of light the two equations are of frequency and wavelength which looks kinda same so if we substitute in all square roots the $v/c$ part we get
\begin{equation} \dfrac{\nu' \text{(emitted)}}{\nu\:\text{(observed)}}=\dfrac{1\!-\!\beta \cos\theta}{\sqrt{1\!-\!\beta^2}} =\dfrac{\lambda\:\text{(observed)}}{\lambda' \text{(emitted)}} \,, \qquad \beta=\dfrac{v}{c} \tag{01}\label{eq01} \end{equation}
Am I right?
