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

1  \(\frac{1}{4}\)  \(\frac{3}{2}\)  \(\frac{1}{2}\)

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

\(\frac{cosθ+sinθ}{cosθ-sinθ}\) = \(\frac{\sqrt {3}+1}{\sqrt {3}-1}\) By componendo & dividendo concept \(\frac{cosθ}{sinθ}\)=\(\frac{\sqrt {3}}{1}\) cotθ = \(\sqrt {3}\) = 30° Now, sinθ = sin30° = \(\frac{1}{2}\)