Trigonometry & Inverse Trigonometry
General
Grade 12
Question:
<p>Number of solutions of <span class="math-inline">\(\sin^{-1}(1-x)-2\sin^{-1}x=\pi/2\)</span>:</p>
Step-by-Step Solution
Key Concept: General
<div class="solution"><p>Test x=0: <span class="math-inline">$\sin^{-1}(1)-0=\pi/2$</span> ✓. Check monotonicity — LHS is strictly decreasing, so only 1 solution.</p><p><strong>Answer: 1 solution (x=0)</strong></p><div class="trap-box"><strong>Trap:</strong> Heavy algebra when endpoint check suffices.</div><div class="key-concept"><strong>Key Concept:</strong> For monotone ITF equations, check simple values first</div></div>
Correct Answer: 1