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If 2y cosq = x sinθ and 2x secθ – y cosecθ = 3 then what is the value of (x² + 4y²) ?
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- 4
- 1
- 2
- 5
Correct Option: A
2y cosθ = x sinθ
| ⇒ x = | .....(i) | |
| sinθ |
∴ 2x secθ – y cosecθ = 3
| ⇒ | - ycosecθ = 3 | |
| sinθ |
⇒ 4y cosecθ – y cosecθ = 3
⇒ 3y cosecθ = 3
| ⇒ y = | = sinθ | |
| cosecθ |
From equation (i),
| x = | = 2cosθ | |
| sinθ |
&therae4; x² + 4y² = (2cosθ)² + 4 sin²θ
= 4 (cos²θ + sin²θ) = 4
