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If x = a (sinθ + cosθ), y = b (sinθ – cosθ) then the value of
x² + y² is a² b²
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- 0
- 1
- 2
- –2
Correct Option: C
x = a (sinθ + cosθ) and
y = b (sinθ – cosθ)
| ⇒ | = sin θ + cos θ and | a |
| = sin θ - cos θ and | b |
| ∴ | + | = (sinθ + cosθ)² +(sinθ – cosθ) 2 | a² | b² |
= sin²θ + cos²θ + 2 sinθ.cosθ +
sin²θ + cos²θ – 2sinθ . cosθ
= 2 (sin²θ + cos²θ) = 2
