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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