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If 3sinθ + 5cosθ = 5, then 5sinθ – 3cosθis equal to
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- ± 3
- ± 5
- 1
- ± 2
Correct Option: A
3 sinθ + 5 cosθ = 5 ...(i)
5 sinθ – 3 cosθ = x ...(ii)
On squaring and adding, 9 sin²θ + 25 cos²θ + 25 sin²θ + 9 cos²θ = 25 + x²
⇒ 9 (sin²θ + cos²θ ) + 25 (cos²θ + sin²θ ) = 25 + x²
⇒ 9 + 25 = 25 + x²
⇒ x² = 9
⇒ x = ±3
