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If |cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t ...

If `|cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n` (a) `x in [-1/3,1/(sqrt(3))]` (b) `x in [-1/(sqrt(3)),1/(sqrt(3))]` `x in [0,1/(sqrt(3))]` (d) none of these

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To solve the inequality \( |\cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right)| < \frac{\pi}{3} \), we will follow these steps: ### Step 1: Understand the range of the inverse cosine function The range of the function \( \cos^{-1}(x) \) is \( [0, \pi] \). Therefore, we can rewrite the inequality without the absolute value: \[ 0 \leq \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right) < \frac{\pi}{3} \] ...
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