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