Question:

<div class="solution"><p><strong>Step 1:</strong> <span class="math-inline">$2\tan^{-1}(1/5)=\tan^{-1}\!\frac{2\cdot(1/5)}{1-(1/5)^2}=\tan^{-1}\!\frac{2/5}{24/25}=\tan^{-1}(5/12)$</span>.</p><p><strong>Step 2:</strong> <span class="math-block">$$\tan\!\left(\tan^{-1}\tfrac{5}{12}-\tfrac{\pi}{4}\right)=\frac{5/12-1}{1+5/12}=\frac{-7/12}{17/12}=-\frac{7}{17}$$</span></p><p><strong>Answer: (A) <span class="math-inline">$-7/17$</span></strong></p><div class="trap-box"><strong>Trap:</strong> Arithmetic errors in the double-angle formula step.</div><div class="key-concept"><strong>Key Concept:</strong> Evaluate nested constants step-by-step using double-angle then subtraction formula</div></div>