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Find domain & range of y = sec-1 x + cosec-1 x + tan-1 x. 

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y = sec-1x + cosec-1x + tan-1x

Domain of sec-1x is R - (2n + 1)\(\frac{\pi}2\); n \(\in\) Z

Domain of cosec-1x is R  - nπ, n \(\in\) Z

Domain of tan-1x is R

\(\therefore\)Domain of y is R - {(2n + 1) \(\frac{\pi}2\), nπ}, n \(\in\) Z

\(\because\) sec-1x + cosec-1x = \(\frac{\pi}2\)

\(\therefore\) y = \(\frac{\pi}2\) + tan-1x

Principal Range of tan-1x is (\(-\frac{\pi}2,\frac{\pi}2\))

\(\therefore\) Range of y is \(\frac{\pi}2+(-\frac{\pi}2,\frac{\pi}2)\) or (0, π).

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