Question

If 3sinθ+5cosθ=5 then 5sinθ−3cosθ=

• A. $\pm 2$
• B. $\pm 3$
• C. $\pm 4$
• D. $\pm 5$

Answer 1

The correct option is B ±3
Let 5sinθ−3cosθ=x Then
Consider (3sinθ+5cosθ)²+(5sinθ−3cosθ)²=9(sin²θ+cos²θ)+25(cos²θ+sin²θ)
(3sinθ+5cosθ)²+(5sinθ−3cosθ)² = 9 + 25 = 34 (sin²θ + cos²θ = 1)
∴x²+25 = 34
x² = 9
x=±3