Question

If 3cosθ + 4sinθ = 5, then what is the value of 3sinθ - 4cosθ = ?

Answer 1

Correct Answer - Option 1 : 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".