Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>The value of \(\cot^{-1}\left(\frac{xy+1}{x-y}\right) + \cot^{-1}\left(\frac{yz+1}{y-z}\right) + \cot^{-1}\left(\frac{zx+1}{z-x}\right)\) is</p>
<p>(a) \(0\)</p>
<p>(b) \(1\)</p>
<p>(c) \(\cot^{-1}x + \cot^{-1}y + \cot^{-1}z\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Recognize the form as differences using inverse cotangent addition formulas
<p>Using the addition formula $\cot^{-1}a - \cot^{-1}b = \cot^{-1}\left(\frac{ab+1}{b-a}\right)$, recognize that each term is a difference of inverse cotangents.</p>
Correct Answer: A