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If A = 2 sin2 x – cos 2x, then A lies in the intervalA. [-1, 3]B. [1, 2]C. [-2, 4]D. None of these |
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Answer» Correct answer is A. Given A = 2 sin2 x – cos 2x [using cos 2x = 1 – 2 sin2 x] so A = 2 sin2 x – cos 2x = 2 sin2 x –[ 1 – 2 sin2 x] = 2 sin2 x -1 + 2 sin2 x] = 4 sin2 x – 1 Now A = 2 sin2 x – cos 2x = 4 sin2 x – 1 As we know sin x lies between -1 and 1 -1 ≤ sin x ≤ 1 0 ≤ sin2x ≤ 1 Multiplying the inequality by 4 0 ≤ 4 sin2 x ≤ 4 Subtracting 1 from the inequality -1 ≤ (4 sin2 x – 1) ≤ 3 From the above inequation, we can say that A = (4 sin2 x – 1) belongs to the closed interval [-1, 3] |
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