Question
If 3 sin θ+5 cos θ=5, which of the following is a possible value of 5 sin θ−3 cos θ?
This question was previously asked in
CDS I 2023 English Previous Year Paper (16-April-2023)
The correct answer is
-3
Let \(u=5\sin\theta-3\cos\theta\). Squaring and adding gives \(5^2+u^2=3^2+5^2=34\), so u=±3. Of the listed choices only −3 is possible; it occurs at θ=0.
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