If \( f(x)=\sin ^{-1} x+\cos ^{-1} x+\tan ^{-1} x+\cot ^{-1} x+\sec ^{-1} x \), then \( f(x) \) ...

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If \( f(x)=\sin ^{-1} x+\cos ^{-1} x+\tan ^{-1} x+\cot ^{-1} x+\sec ^{-1} x \), then \( f(x) \) lies in the interval
(a) \( [\pi, 2 \pi] \)
(b) \( (\pi, 2 \pi) \)
(c) \( \left[\pi, \frac{3 \pi}{2}\right) \cup\left(\frac{3 \pi}{2}, 2 \pi\right] \)
(d) None of these
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