If 8cotθ = 6, then the value of $\frac{sinθ+cosθ}{sinθ-cosθ}$ is :

7

 8cotθ = 6

cotθ =  \(\frac{6}{8}\)

B = 6 & P = 8

P² + B² = H²

8² + 6² = H²

H = 10

sinθ + cosθ = \(\frac{8}{10}\) + \(\frac{6}{10}\)  = \(\frac{14}{10}\) 

sinθ - cosθ = \(\frac{8}{10}\) - \(\frac{6}{10}\) = \(\frac{2}{10}\)

Now , \(\frac{sinθ + cosθ}{sinθ -cosθ}\)

=\(\frac{14}{2}\)

= 7