Inverse Trigonometric Functions
Equations and Domain
Premium Question
Grade 12
Question:
Find the number of real solutions of $\sin^{-1}|x - 1| + \cos^{-1}|x - 2| = \frac{\pi}{2}$.
Step-by-Step Solution
Key Concept: Use $\cos^{-1}(t) = \pi/2 - \sin^{-1}(t)$ to simplify. The equation collapses to $|x - 1| = |x - 2|$. Verify the solution lies in the valid domain.
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Correct Answer: 1