Explanation

Given, $x = \cos(\omega t + kx)$ Here, $(\omega t + kx)$ is an angle so the dimension of $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\omega t + kx) = \left\lbrack M^{0}L^{0}T^{0} \right\rbrack$ Or dimensions of $\omega t = \left\lbrack M^{0}L^{0}T^{0} \right\rbrack$ Or dimensions of $\omega = \frac{\left\lbrack M^{0}L^{0}T^{0} \right\rbrack}{\lbrack T\rbrack}$ Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack M^{0}L^{0}T^{- 1} \right\rbrack$