Trigonometry & Inverse Trigonometry
General
Grade 12
Question:
<p>If \(\tan^{-1}x+\tan^{-1}y+\tan^{-1}z=\pi/2\), then \(xy+yz+zx=\)</p>
0
<strong>1</strong>
-1
xyz
Step-by-Step Solution
<div class="solution"><p>Sum formula: $\tan(\sum\tan^{-1})=\frac{x+y+z-xyz}{1-(xy+yz+zx)}$. For sum = \pi/2, denominator = 0: $xy+yz+zx=1$.</p><p><strong>Answer: (2) 1</strong></p><div class="key-concept"><strong>Key Concept:</strong> Sum of tan⁻^1 = \pi/2 \to denominator of addition formula = 0
Correct Answer: 2