Trigonometry & Inverse Trigonometry
General
Grade 12
Question:
<p>If \(\cos^{-1}x+\cos^{-1}y+\cos^{-1}z=3\pi\), then \(xy+yz+zx=\)</p>
Step-by-Step Solution
<div class="solution"><p>Each $\cos^{-1}$ term has max value $\pi$. Sum = $3\pi$ forces each = $\pi$, so $x=y=z=-1$. Then $xy+yz+zx=3$.</p><div class="key-concept"><strong>Key Concept:</strong> Bounded sum at maximum forces every term to its maximum
Correct Answer: 3