1.

Range of sin^(-1)((x^(2)+1)/(x^(2)+2)) is

Answer»

`[0,(pi)/(2)]`
`(0,(pi)/(6)`
`[(pi)/(6),(pi)/(2))`
None of these

Solution :Here, `(X^(2)+1)/(x^(2)+2)=1-(1)/(x^(2)+2)`
Now, `2 le x^(2)+2lt oo` for all x ein R
`implies(1)/(2)GE (1)/(x^(2)+2)GT0`
`implies -(1)/(2) le (-1)/(x^(2)+2) lt 0`
`implies(1)/(2) le 1-(1)/(x^(2)+2)lt`
`implies (pi)/(6) le sin^(-1)(1-(1)/(x^(2)+2))lt(pi)/(2)`


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