A physical quantity x depends on quantities y and z as follows: x= Ay + B tan Cz, where A, B and C are constants. Which of the following do not have the same dimensions?

x = Ay + B tan Cz

From the dimensional homogeneity

[x] = [Ay] = [B]  $\Rightarrow$ $\left[\frac{\mathrm{x}}{\mathrm{A}}\right] = \left[\mathrm{y}\right] = \left[\frac{\mathrm{B}}{\mathrm{A}}\right]$

$\left[\mathrm{Cz}\right] = \left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\right]$= Dimension less

x and B; C and ${\mathrm{Z}}^{-1}$; y and $\frac{\mathrm{B}}{\mathrm{A}}$have the same dimension but x and A have different dimension