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If x = sin θ + cos θ and y = sin θ – cos θ, then the value of (x2 + y2 - 1) × (x2 + y2 + 5) will be

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If x = sin θ + cos θ and y = sin θ – cos θ, then the value of (x2 + y2 - 1) × (x2 + y2 + 5) will be
1). 6
2). 9
3). 7
4). 10


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1 answers

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Answered by on | Votes 0 |

Given, x = sin θ + cos θ and y = sin θ – cos θ

Thus, x + y = 2sinθ

Also, xy = sin2θ – cos2θ

(x + y)2 = x2 + y2 + 2xy

⇒ 4sin2θ = x2 + y2 + 2sin2θ – 2cos2θ

⇒ x2 + y2 = 2(sin2θ + cos2θ) = 2

Thus, (x2 + y2 – 1) × (x2 + y2 + 5) = (2 – 1) × (2 + 5) = 7

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