If $$\tan \theta = \frac{20}{21}$$, then the value of $$\frac{\sin \theta - \cos \theta}{\sin \theta + \cos \theta}$$ is:

Given,  $$\tan\theta=\frac{20}{21}$$

$$\frac{\sin\theta-\cos\theta}{\sin\theta+\cos\theta}=\frac{\cos\theta\ \left(\frac{\sin\theta\ }{\cos\theta\ }-1\right)}{\cos\theta\ \left(\frac{\sin\theta\ }{\cos\theta\ }+1\right)}$$

$$=\ \frac{\tan\theta\ -1}{\tan\theta\ +1}$$

$$=\ \frac{\frac{20}{21}\ -1}{\frac{20}{21}\ +1}$$

$$=\ \frac{\frac{20-21}{21}}{\frac{20+21}{21}}$$

$$=\ \frac{-1}{41}$$

Hence, the correct answer is Option B