Question:

<div class="solution"><p><strong>Step 1:</strong> Let \(\theta=\frac{1}{2}\cos^{-1}x\) so \(\cos 2\theta=x\).</p><p><strong>Step 2:</strong> <span class="math-block">\[\tan(\pi/4+\theta)+\tan(\pi/4-\theta)=\frac{1+\tan\theta}{1-\tan\theta}+\frac{1-\tan\theta}{1+\tan\theta}=\frac{2(1+\tan^2\theta)}{1-\tan^2\theta}=\frac{2}{\cos 2\theta}=\frac{2}{x}\]</p><p><strong>Answer: (C) \(2/x\)</strong></p><div class="trap-box"><strong>Trap:</strong> Confusing with x or 2x -- the cos 2\theta = x appears in the denominator.<div class="key-concept"><strong>Key Concept:</strong> \(\tan(\pi/4+\theta)+\tan(\pi/4-\theta)=2\sec 2\theta\)