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 $\sec \theta$?

$\frac{2\sqrt3}{3}$

\(\frac{cosθ + sinθ}{cosθ - sinθ}\) = \(\frac{√3+ 1}{√3- 1}\)

By applying componendo and dividendo ,

\(\frac{2cosθ }{2 sinθ}\) = \(\frac{2√3}{2}\)

cotθ  = √3

{ using , cot30º  = √3  }

Now,

secθ 

= sec30º

= \(\frac{2}{√3}\)

= \(\frac{2√3}{3}\)