Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions - Properties
Grade 12
Question:
<p>If \(\cot^{-1}\left(\frac{n}{p}\right) = \frac{p}{6}\), \(n \in \mathbb{N}\), then the maximum value of \(\tan^{-1}x + \cot^{-1}\left(\frac{1}{y}\right) = \sin^{-1}\left(\frac{3}{10}\right)\) is \('n'\) is</p>
<p>(a) 1</p>
<p>(b) 5</p>
<p>(c) 9</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Use properties of inverse trigonometric functions and their relationships to find the maximum natural number value.
<p>Based on the given conditions with inverse trigonometric functions and the constraint that \(n \in \mathbb{N}\), solving yields \(n = 5\) as the maximum value.</p>
Correct Answer: B