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Question

If 3sinθ+5cosθ=5 then 5sinθ3cosθ=
  1. ±2
  2. ±3
  3. ±4
  4. ±5

A
±2
B
±5
C
±3
D
±4
Solution
Verified by Toppr

The correct option is B ±3
Let 5sinθ3cosθ=x Then
(3sinθ+5cosθ)2+(5sinθ3cosθ)2=9(sin2θ+cos2θ)+25(cos2θ+sin2θ)
=9+25=34
x2+25=34orx2=9orx=±3

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