Please solve this question?

Dear Student, 
Solution)
$\underset{x\to 0}{\lim }\frac{1-\cos ax}{1-\cos bx}$
Here we can write the given limits as;
$$\begin{gathered} \underset{ax\to 0}{\lim }\frac{1-\cos ax}{ax}\times ax\times \underset{ax\to 0}{\lim }\frac{bx}{1-\cos bx}\times \frac{1}{bx} \\ = \frac{ax}{bx}\times \underset{ax\to 0}{\lim }\frac{1-\cos ax}{ax}\times \underset{ax\to 0}{\lim }\frac{bx}{1-\cos bx} \\ =0 .............\{\mathrm{Since} \underset{x\to 0}{\lim }\frac{1-\cos x}{x} = 0\} \end{gathered}$$
Therefore, $\underset{x\to 0}{\lim }\frac{1-\cos ax}{1-\cos bx}$ = 0
Regards!