If $$\sec \theta - \tan \theta = 3$$, then $$\cos \theta$$ is equal to:

$$\sec\theta-\tan\theta=3$$ ...................(1)

$$=$$>  $$\left(\sec\theta-\tan\theta\right)\times\frac{\left(\sec\theta+\tan\theta\right)}{\left(\sec\theta+\tan\theta\right)}=3$$

$$=$$>  $$\frac{\sec^2\theta-\tan^2\theta}{\left(\sec\theta+\tan\theta\right)}=3$$

$$=$$>  $$\frac{1}{\left(\sec\theta+\tan\theta\right)}=3$$

$$=$$>  $$\sec\theta+\tan\theta=\frac{1}{3}$$ ...........(2)

Adding (1) and (2)

$$=$$>  $$2\sec\theta=3+\frac{1}{3}$$

$$=$$>  $$2\sec\theta=\frac{10}{3}$$

$$=$$>  $$\sec\theta=\frac{5}{3}$$

$$=$$>  $$\cos\theta=\frac{3}{5}$$

Hence, the correct answer is Option C