An object takes n times as much as to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by :

Question

$$\begin {array} {1 1} (1)\;\bigg ( 1-\frac{1}{n^2}\bigg) & \quad (2)\;\bigg ( \frac{1}{1-n^2}\bigg) \\ (3)\;\sqrt {1-\frac{1}{n^2}} & \quad (4)\;\sqrt { 1+\frac{1}{n^2}} \end {array}$$