CDS 2026 · PYQ · Trigonometry · medium
If 3sinθ + 4cosθ = 5, then what is the value of 4tanθ + 3cotθ?
- A.7✓ Correct
- B.8
- C.9
- D.10
Given 3sinθ + 4cosθ = 5. Since maximum of 3sinθ + 4cosθ is √(9+16) = 5, equality occurs when sinθ/3 = cosθ/4, i.e., tanθ = 3/4. So sinθ = 3/5, cosθ = 4/5, tanθ = 3/4, cotθ = 4/3. Then 4tanθ + 3cotθ = 4(3/4) + 3(4/3) = 3 + 4 = 7.
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