Trigonometry & Inverse Trigonometry
General
Grade None
Question:
<p>If \(\sum_{i=1}^{10}\sin^{-1}x_i=5\pi\), then \(\sum_{i=1}^{10}x_i^2=\)</p>
0
<strong>10</strong>
5
100
Step-by-Step Solution
<div class="solution"><p>Max value of each $\sin^{-1}x_i=\pi/2$. Sum = $10\times\pi/2=5\pi$ only if every $x_i=1$. So $\sum x_i^2=10$.</p><p><strong>Answer: (2) 10</strong></p><div class="trap-box"><strong>Trap:</strong> Bounded sum at maximum forces every term to its maximum -- no averaging possible.<div class="key-concept"><strong>Key Concept:</strong> Extreme sum of bounded terms forces every term to the extreme
Correct Answer: 2