If

Question:

If $f(x)=\frac{1-x}{1+x}$, then fof $(\cos 2 \theta)=$ ______________.

Solution:

Given: $f(x)=\frac{1-x}{1+x}$

$f o f(\cos 2 \theta)=f(f(\cos 2 \theta))$

$=f\left(\frac{1-\cos 2 \theta}{1+\cos 2 \theta}\right)$

$=f\left(\frac{2 \sin ^{2} \theta}{2 \cos ^{2} \theta}\right)$

$=f\left(\tan ^{2} \theta\right)$

$=\frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}$

$=\cos 2 \theta$

Hence, fof $(\cos 2 \theta)=\cos 2 \theta$.

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