If 3cosθ + 4sinθ = 5, then what is the value of 3sinθ - 4cosθ = ?
If 3cosθ + 4sinθ = 5, then what is the value of 3sinθ - 4cosθ = ? Correct Answer 0
Given:
3cosθ + 4sinθ = 5
Calculation:
⇒ 3cosθ + 4sinθ = 5
⇒ 9cos2θ + 16sin2θ + 24cosθ sinθ = 25 (By squaring the both side)
⇒ 9 × (1 - sin2θ) + 16 × (1 - cos2θ) + 24 × cosθ × sinθ = 25
⇒ 9sin2θ - 24 cosθ × sinθ + 16 cos2θ = 0
⇒ (3sinθ - 4cosθ)2 = 0
⇒ 3sinθ - 4cosθ = 0
∴ The required result will be "0".
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Feb 20, 2025