Question:

<div class="solution"><p><span class="math-inline">$\cos^{-1}\!\sqrt{p}+\sin^{-1}\!\sqrt{p}=\pi/2$</span> (complementary pair since <span class="math-inline">$\cos^{-1}\!\sqrt{1-p}=\sin^{-1}\!\sqrt{p}$</span>). So <span class="math-inline">$\pi/2+\cos^{-1}\!\sqrt{1-q}=3\pi/4\implies\cos^{-1}\!\sqrt{1-q}=\pi/4\implies\sqrt{1-q}=1/\sqrt{2}\implies q=1/2$</span>.</p><p><strong>Answer: (2) 1/2</strong></p><div class="trap-box"><strong>Trap:</strong> Trying to solve for p as well — the p-terms collapse immediately.</div><div class="key-concept"><strong>Key Concept:</strong> Complementary pair cos⁻¹√p + cos⁻¹√(1-p) = π/2</div></div>