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Range of sin^(-1)((x^(2)+1)/(x^(2)+2)) is |
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Answer» `[0,(pi)/(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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