InterviewSolution
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InterviewSolution
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The set of all `x`in the interval `[0,pi]`for which `2sin^2x-3sinx+1geq0`is______ |
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Answer» Correct Answer - `x in [0,(pi)/(6)]uu{(pi)/(2)} uu [(5pi)/(6),pi]` Given, ` 2 sin ^(2) x - 3 sin x + 1 ge 0` ` rArr 2 sin ^(2) x - 2 sin x - sin x + 1 ge 0 ` ltBrgt ` rArr " " ( 2 sin x - 1 ) (sin x - 1 ) ge 0 ` ` rArr 2 sin x - 1 le 0 or sin x ge 1 ` ` rArr " " sin x le (1)/(2) or sin x = 1 ` ` rArr " "x in [0, (pi)/(6)] uu {(pi)/(2)} uu [ (5pi)/(6), pi]` |
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