If - = 1 3 , the value of . = ?

Answer: Option C

$$\begin{array}{rl}& \mathbf{Shortcut}\mathbf{method}:\\ & \text{Put }\theta =30^{\circ }\\ & \Rightarrow \sec \theta -\tan \theta =\frac{1}{\sqrt{3}}\\ & \Rightarrow \sec 30^{\circ }-\tan 30^{\circ }=\frac{1}{\sqrt{3}}\\ & \Rightarrow \frac{2}{\sqrt{3}}-\frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}\\ & \Rightarrow \frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}\left(\text{Satisfied}\right)\\ & \sec \theta =30^{\circ }\\ & \Rightarrow \sec \theta .\tan \theta \\ & \Rightarrow \sec 30^{\circ }.\tan 30^{\circ }\\ & \Rightarrow \frac{2}{\sqrt{3}}\times \frac{1}{\sqrt{3}}\\ & \Rightarrow \frac{2}{3}\end{array}$$