In terms of time t and distance x, the force F is given by F = A sin Ct + B cos Dx, then dimensions of ABand CD are given by  [UK PMT 2015]

Given, F = A sin Ct + B cos Dxwhere, t = time and x = distance                     ... (i)As, we know that trigonometric ratios are dimensionless. This implies     sin Ct = dimensionless and cos Dx = dimensionlessAlso,  [C]=1t=T-1 and [D]=1x=L-1As, Eq. (i) represents the force. So, A and B both have the dimensions as that of force. So, A/B is dimensionless, i.e. [M0L0T0].While CD=T-1 L-1=M0LT-1