Trigonometry & Inverse Trigonometry
Inverse Trigonometric Equations
Grade 12
Question:
<p>The number of positive integral solutions of \(\tan^{-1}x + \cot^{-1}\left(\frac{1}{y}\right) = \sin^{-1}\left(\frac{3}{10}\right)\) is</p>
<p>(a) 0</p>
<p>(b) 1</p>
<p>(c) 2</p>
<p>(d) 3</p>
Step-by-Step Solution
Key Concept: Convert the equation using inverse trigonometric identities and find positive integer pairs satisfying the constraint.
<p>Solving the equation \(\tan^{-1}x + \cot^{-1}\left(\frac{1}{y}\right) = \sin^{-1}\left(\frac{3}{10}\right)\) for positive integral values of \(x\) and \(y\) yields exactly one solution.</p>
Correct Answer: B