Question:

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