Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>Let \(f(x) = \sin^{-1}x - \cos^{-1}x\), then the set of values of \(k\) for which \(|f(x)| = k\) has exactly two distinct solutions is:</p>
<p>(a) \(\left(0, \frac{\pi}{2}\right]\)</p>
<p>(b) \(\left(0, \frac{\pi}{2}\right)\)</p>
<p>(c) \(\left[\frac{\pi}{2}, \frac{3\pi}{2}\right)\)</p>
<p>(d) \(\left[\pi, 3\right]\)</p>
Step-by-Step Solution
Key Concept: Analyze the function \(f(x) = \sin^{-1}x - \cos^{-1}x\) using the identity \(\sin^{-1}x + \cos^{-1}x = \pi/2\) to find its range and behavior, then determine when \(|f(x)| = k\) has exactly two solutions.
<p>Solution not provided in source text.</p>
Correct Answer: a