If f(x) = frac{1 - x}{1 + x}, then f(f(cos x) | vedclass

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(A) Given $f(x) = \frac{1 - x}{1 + x}$.First, calculate $f(\cos x) = \frac{1 - \cos x}{1 + \cos x}$.Using trigonometric identities $1 - \cos x = 2 \si

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$\cos x$

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(A) Given $f(x) = \frac{1 - x}{1 + x}$.First, calculate $f(\cos x) = \frac{1 - \cos x}{1 + \cos x}$.Using trigonometric identities $1 - \cos x = 2 \sin^2 \frac{x}{2}$ and $1 + \cos x = 2 \cos^2 \frac{x}{2}$, we get $f(\cos x) = \frac{2 \sin^2 (x/2)}{2 \cos^2 (x/2)} = 	an^2 \frac{x}{2}$.Now, calculate $f(f(\cos x)) = f(	an^2 \frac{x}{2}) = \frac{1 - 	an^2 (x/2)}{1 + 	an^2 (x/2)}$.Using the identity $\cos 2	heta = \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta}$, where $	heta = \frac{x}{2}$, we get $f(f(\cos x)) = \cos(2 \cdot \frac{x}{2}) = \cos x$.

If $f(x) = \frac{1 - x}{1 + x}$, then $f(f(\cos x)) = $

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