If \(\frac{cosθ+sinθ}{cosθ-sinθ}\) = \(\frac{\sqrt {3}+1}{\sqrt {3}-1}\), 0° < θ < 90°, then find the value of secθ.

\(\frac{2\sqrt {3}}{3}\)

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

By componendo & dividendo concept

\(\frac{cosθ}{sinθ}\)=\(\frac{\sqrt {3}}{1}\)

cotθ = \(\sqrt {3}\) = 30°

Now, secθ =\(\frac{2}{\sqrt {3}}\)×\(\frac{\sqrt {3}}{\sqrt {3}}\)

= \(\frac{2\sqrt {3}}{3}\)