If $$(\cos \theta + \sin \theta) : (\cos \theta - \sin \theta) = (\sqrt{3} + 1) : (\sqrt{3} - 1), 0^\circ < \theta < 90^\circ$$, then what is the value of $$\sec \theta$$?

Given that $$(\cos \theta + \sin \theta) : (\cos \theta - \sin \theta) = (\sqrt{3} + 1) : (\sqrt{3} - 1)$$

$$\Rightarrow  \sqrt{3} \cos \theta - \cos \theta + \sqrt{3} \sin \theta - \sin \theta = \sqrt{3} \cos \theta + \cos \theta - \sqrt{3} \sin \theta - \sin \theta $$

$$\Rightarrow 2 \sqrt {3} \sin \theta = 2 \cos \theta $$

$$\Rightarrow \tan \theta = \dfrac {1}{\sqrt {3}} $$

$$\Rightarrow \theta = \tan^-1 \dfrac{1} {\sqrt {3}}$$

$$\Rightarrow \theta = 30^{\circ} $$

then $$ \sec \theta = \sec \30^\circ$$

                             = $$ \dfrac{2} {\sqrt {3}} $$ Ans