$f\left(x\right)=\frac{1-\cos \left(1-\mathrm{cosx}\right)}{{\mathrm{x}}^4}$ is continuous at $\mathrm{x}=0$ then $f\left(0\right)=$

$\mathrm{f}\left(\mathrm{x}\right)=\frac{1-\cos (1-\cos x)}{{\mathrm{x}}^4}$ is continuous at x = 0

$\Rightarrow \mathrm{f}\left(\mathrm{o}\right)=\underset{\mathrm{x}\to 0^{\mathrm{ }}}{\lim }\mathrm{f}\left(\mathrm{x}\right)=\underset{\mathrm{x}\to 0^{\mathrm{ }}}{\lim }\frac{1-\cos (1-\mathrm{cosx})}{{\mathrm{x}}^4}$

$=\underset{\mathrm{x}\to 0^{\mathrm{ }}\mathrm{ }}{\lim }\frac{1-\cos \left(1-\mathrm{cosx}\right)}{{\left(1-\mathrm{cosx}\right)}^2}\times {\left(\frac{1-\mathrm{cosx}}{{\mathrm{x}}^2}\right)}^2\mathrm{ }$

$=\frac{1}{2}{\left(\frac{1}{2}\right)}^2=\frac{1}{8}$

Option (4) is correct