1
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Question

# If sin2θ=x2−4x+5,then x=

A
0,1
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B
2
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C
2,2
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Solution

## The correct option is B 2Given: sin2θ=x2−4x+5 Now, x2−4x+5 has complex roots as it's discriminant D=16−20=−4<0 Also, coefficient of x2 is positive. ⇒x2−4x+5 is upward opening curve. Now, it's minimum point is given by the relation: (−b2a,−D4a) Equating the values of a,b,c, we get the coordinates of minimum point as: (−(−4)2,−(−4)4)≡(2,1) Hence, at x=2, the quadratic equation is minimum and have a value 1. Also, we know −1≤sinθ≤1 Or 0≤sin2θ≤1 Thus, for sin2θ=x2−4x+5 This is possible only when x2−4x+5=1 or at x=2.

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