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What is the correct value of \(\sin(\cos^{-1}x)\) when \(x\in[-1,1]\)?\(\sin(\cos^{-1}x)\) का सही मान क्या है, जब \(x\in[-1,1]\)?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\sqrt{1-x^2})(\sqrt{1-x^2})
If \(\theta=\cos^{-1}x\), then \(\theta\in[0,\pi]\) and \(\sin\theta\ge0\). Hence the value is \(\sqrt{1-x^2}\).यदि \(\theta=\cos^{-1}x\), तो \(\theta\in[0,\pi]\) और \(\sin\theta\ge0\)। इसलिए मान \(\sqrt{1-x^2}\) है।
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