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If log cos x sin x>=2 and 0 π then sin x is in the interval (a)[(5 1/2 -1)/2,1] (b)(0,5 1/2 -1)/2] (c)[0,1/2] (d)none

If logcos x sin x>=2 and 0<=x<=3π then sin x is in the interval


(a)[(51/2-1)/2,1]


(b)(0,51/2-1)/2]


(c)[0,1/2]


(d)none

Grade:12

1 Answers

sahil doshi
8 Points
12 years ago

logcos xsin x >=2

sin x >= cos2x

sin x >= 1 - sin2x

sin2x + sin x - 1 >= 0

[sin x - (51/2-1) / 2] * [sin x - (-51/2-1) / 2] >= 0

now, sin x > -1

therefore [sin x - (-51/2-1)/2] > 0       { 51/2 ≈ 2        therefore    -(-51/2-1)/2 ≈ 1.5}

therefore [sin x - (51/2-1) / 2] should be > 0

sin x > (51/2-1) / 2]

and sin x lies between [-1,1]

(a)[(51/2-1)/2,1]

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