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What is the value of \(\cos\left(\sin^{-1}x\right)\) when \(x\in\left[-1,1\right]\)?\(\cos\left(\sin^{-1}x\right)\) 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 \(\theta=\sin^{-1}x\), then \(\sin\theta=x\) and \(\theta\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\). Here \(cos\theta\ge0\), so \(\sqrt{1-x^2}\) is correct.यदि \(\theta=\sin^{-1}x\), तो \(sin\theta=x\) और \(\theta\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)। यहाँ \(cos\theta\ge0\), इसलिए \(\sqrt{1-x^2}\) सही है।
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