If (sinα)x2−2x+b≥2 for all the real values of x≥1 and αϵ(0,π/2)∪(π/2,π), then the possible real values of b lies in
A
(2,4)
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B
(3,4)
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C
(4,5)
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D
(5,8)
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Solution
The correct option is A(3,4) The minimum value of the quadratic takes place at 1sinα which is less than 1. Thus, we check at 1 and then it should be valid for all x greater than 1. Thus, sinα−2+b>2 ⇒b≥4−sinα ∴b∈(3,4)