1. We are given the function $$f(x) = \frac{\sin x - \cos x}{\sin x + \cos x}$$ and asked to analyze or simplify it. 2. The goal is to simplify the expression by using trigonometric identities and algebraic manipulation. 3. Recall the identity for tangent of a difference: $$\tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$$. We can try to rewrite numerator and denominator in terms of sine and cosine to find a simpler form. 4. Divide numerator and denominator by $$\cos x$$ (assuming $$\cos x \neq 0$$): $$f(x) = \frac{\frac{\sin x}{\cos x} - 1}{\frac{\sin x}{\cos x} + 1} = \frac{\tan x - 1}{\tan x + 1}$$ 5. Recognize that $$\frac{\tan x - 1}{\tan x + 1} = \tan\left(x - \frac{\pi}{4}\right)$$ using the tangent subtraction formula: $$\tan\left(x - \frac{\pi}{4}\right) = \frac{\tan x - \tan \frac{\pi}{4}}{1 + \tan x \tan \frac{\pi}{4}} = \frac{\tan x - 1}{1 + \tan x}$$ 6. Notice the denominator in our expression is $$\tan x + 1$$, but the formula has $$1 + \tan x$$ which is the same due to commutativity of addition. 7. Therefore, the simplified form is: $$f(x) = \tan\left(x - \frac{\pi}{4}\right)$$ 8. This means the function $$f(x)$$ is equivalent to the tangent function shifted by $$\frac{\pi}{4}$$ to the right. Final answer: $$f(x) = \tan\left(x - \frac{\pi}{4}\right)$$