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

\(\frac{1}{2}\)

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

By componendo & dividendo concept

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

cotθ = \(\sqrt {3}\) = 30°

Now, sinθ = sin30° 

= \(\frac{1}{2}\)