Mathematics

Mathematics

Problem

Match the principal values of cos⁡−1(8x4−8x2+1)\cos^{-1}(8x^4 - 8x^2 + 1) given in column I with the corresponding intervals of xx given in column II, for which it holds.
Column IColumn II
A 4cos⁡−1x4 \cos^{-1} xP. 0≤x≤120 \le x \le \frac{1}{\sqrt{2}}
B 4cos⁡−1x−2π4 \cos^{-1} x - 2\piQ. 12≤x≤1\frac{1}{\sqrt{2}} \le x \le 1
C 2π−4cos⁡−1x2\pi - 4 \cos^{-1} xR. −1≤x≤−12-1 \le x \le -\frac{1}{\sqrt{2}}
D 4π−4cos⁡−1x4\pi - 4 \cos^{-1} xS. −12≤x≤0-\frac{1}{\sqrt{2}} \le x \le 0

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