Question:

<div class="solution"><p><strong>Step 1:</strong> <span class="math-inline">$5\in(3\pi/2,2\pi)$</span> so <span class="math-inline">$\sin^{-1}(\sin 5)=5-2\pi$</span>.</p><p><strong>Step 2:</strong> Inequality: <span class="math-inline">$x^2-4x+(2\pi-5)<0$</span>.</p><p><strong>Step 3:</strong> Roots: <span class="math-inline">$x=2\pm\sqrt{9-2\pi}$</span>.</p><p><strong>Answer: (A) <span class="math-inline">$x\in(2-\sqrt{9-2\pi},\,2+\sqrt{9-2\pi})$</span></strong></p><div class="trap-box"><strong>Trap:</strong> Taking <span class="math-inline">$\sin^{-1}(\sin 5)=5$</span> — wrong because 5 is outside the principal range <span class="math-inline">$[-\pi/2,\pi/2]$</span>.</div><div class="key-concept"><strong>Key Concept:</strong> Always reduce angle to principal branch before solving ITF inequalities</div></div>