If $\frac{cosθ+sinθ}{cosθ-sinθ}=8$, then the value of cot θ is equal to :

$\frac{6}{5}$ $\frac{9}{7}$ $\frac{8}{7}$ $\frac{7}{6}$

$\frac{9}{7}$

\(\frac{cosθ + sinθ }{cosθ - sinθ }\) = 8 By applying Dividendo and Componendo \(\frac{cosθ + sinθ + cosθ - sinθ }{cosθ + sinθ - cosθ + sinθ }\) =  \(\frac{8+1 }{8-1}\) \(\frac{cosθ  }{ sinθ  }\) =  \(\frac{9 }{7}\) cot θ = \(\frac{9 }{7}\)