Question:

<div class="solution"><p><strong>Step 1:</strong> Recognize <span class="math-inline">\(\sin^{-1}\!\sqrt{x/2}+\cos^{-1}\!\sqrt{x/2}=\pi/2\)</span> (complementary pair).</p><p><strong>Step 2:</strong> <span class="math-inline">\(\pi/2+\tan^{-1}y=2\pi/3\implies\tan^{-1}y=\pi/6\implies y=1/\sqrt{3}\)</span>.</p><p><strong>Step 3:</strong> Domain: <span class="math-inline">\(0\le x\le 4\)</span>. So <span class="math-inline">\(x^2\in[0,16]\)</span>.</p><p>Max: <span class="math-inline">\(16+1/3=49/3\)</span> ✓. Min: <span class="math-inline">\(0+1/3=1/3\)</span> ✓.</p><p><strong>Answer: Both (A) and (B)</strong></p><div class="trap-box"><strong>Trap:</strong> The first two terms don't vary independently — they collapse to a constant via the complementary identity.</div><div class="key-concept"><strong>Key Concept:</strong> Complementary sin⁻¹+cos⁻¹=π/2 collapses multi-variable equations</div></div>