One branch of cos^-1 other than the principal value branch corresponds to
$(a) [\frac{π}{2}, \frac{3 π}{2}] (b) [π, 2 π] - \{\frac{3 π}{2}\} (c) (0, π) (d) [2 π, 3 π]$

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Solution

The domain of the function $f (x) = \cos^{- 1} x$ is $[- 1, 1]$ . The range of $\cos^{- 1} x$ in one of the intervals $. . ., [- π, 0], [0, π], [π, 2 π], [2 π, 3 π], . . .$ is one-one and onto with the range $[- 1, 1]$ .

Thus, one branch of cos⁻¹x other than the principal value branch corresponds to $[2 π, 3 π]$ .

Hence, the correct answer is option (d).

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