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What is the correct value of \(\cos(\sin^{-1}x)\) when \(x\in[-1,1]\)?\(\cos(\sin^{-1}x)\) 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=\sin^{-1}x), then (\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]) and (\cos\theta\ge0). So the positive root should be taken.यदि (\theta=\sin^{-1}x), तो (\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]) और (\cos\theta\ge0)। इसलिए positive root लेना चाहिए।
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