Inverse Trigonometric Functions
Xam Idea
CBSE
Grade 12
Question:
Find the maximum and minimum values of $(\sin^{-1} x)^2 + (\cos^{-1} x)^2$.
Step-by-Step Solution
Key Concept: Rewrite as (\pi/2)^2 - 2 \sin^{-1} x \cos^{-1} x. Min at \sin^{-1} x = \pi/4 is \pi^2/8. Max at \sin^{-1} x = -\pi/2 is 5\pi^2/4.
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Correct Answer:
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