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If -1le x le -(1)/(sqrt(2)) , then prove...

If `-1le x le -(1)/(sqrt(2))` , then prove that `sin^(-1)(2xsqrt(1-x^2))=-2pi+2cos^(-1)x`.

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To prove that \( \sin^{-1}(2x\sqrt{1-x^2}) = -2\pi + 2\cos^{-1}(x) \) for \( -1 \leq x \leq -\frac{1}{\sqrt{2}} \), we will follow these steps: ### Step 1: Start with the given equation We want to prove: \[ \sin^{-1}(2x\sqrt{1-x^2}) = -2\pi + 2\cos^{-1}(x) \] ...
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