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).