Question:

<div class="solution"><p><strong>Step 1:</strong> <span class="math-inline">$2\tan^{-1}(1)=2\cdot\pi/4=\pi/2$</span>.</p><p><strong>Step 2:</strong> <span class="math-inline">$\sin^{-1}(x^2-5x+7)=\pi/2\implies x^2-5x+7=1$</span>.</p><p><strong>Step 3:</strong> <span class="math-inline">$x^2-5x+6=0\implies(x-2)(x-3)=0\implies x=2,3$</span>.</p><p><strong>Answer: (A),(B) → x=2 and x=3</strong></p><div class="trap-box"><strong>Trap:</strong> Forgetting to verify the argument stays in [-1,1] — here it's forced to 1, so valid.</div><div class="key-concept"><strong>Key Concept:</strong> Map the constant RHS to its unit-circle value first</div></div>