Question:

<div class="solution"><p><strong>Step 1:</strong> $\tan^{-1}1+\tan^{-1}(1/2)=\tan^{-1}\!\frac{3/2}{1/2}=\tan^{-1}3$.</p><p><strong>Step 2:</strong> $\tan^{-1}3+\tan^{-1}(1/3)=\pi/2$ (since $3\times(1/3)=1>0$, complementary pair).</p><p><strong>Answer: \pi/2</strong></p><div class="trap-box"><strong>Trap:</strong> The second step uses the special case tan⁻^1t + tan⁻^1(1/t) = \pi/2 for t>0.<div class="key-concept"><strong>Key Concept:</strong> $\tan^{-1}t+\tan^{-1}(1/t)=\pi/2$ for $t>0$