Question:
For \(x\in[-1,1]\), evaluate \(\ \sin\!\big(2(\sin^{-1}x+\cos^{-1}x)\big)\).
For \(x\in[-1,1]\), evaluate \(\ \sin\!\big(2(\sin^{-1}x+\cos^{-1}x)\big)\).
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Key identity: $\sin^{-1}x+\cos^{-1}x=\dfrac{\pi}{2}$ for all $x\in[-1,1]$.
Updated On: Oct 17, 2025
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The Correct Option is A
Solution and Explanation
\(\sin^{-1}x+\cos^{-1}x=\dfrac{\pi}{2}\). Hence
\[
2(\sin^{-1}x+\cos^{-1}x)=2\cdot \frac{\pi}{2}=\pi,
\sin(\pi)=0.
\]
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