KCET · Maths · Indefinite Integration
If \( \alpha \leq 2 \sin ^{-1} x+\cos ^{-1} x \leq \beta \), then
- A \( \alpha=-\frac{\pi}{2} \quad \beta=\frac{\pi}{2} \)
- B \( \alpha=-\frac{\pi}{2} \quad \beta=\frac{3 \pi}{2} \)
- C \( \alpha=0 \quad \beta=\pi\)
- D \( \alpha=0 \quad \beta=2 \pi \)
Answer & Solution
Correct Answer
(C) \( \alpha=0 \quad \beta=\pi\)
Step-by-step Solution
Detailed explanation
\( 2 \sin^{-1} x+\cos^{-1} x = \sin^{-1} x + (\sin^{-1} x + \cos^{-1} x) \) \( = \sin^{-1} x + \frac{\pi}{2} \)
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