If 3sinθ + 4cosθ = 5, then what is the value of 4tanθ + 3cotθ?
Answer
The correct answer is A: 7. 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.
A.7✓ Correct
B.8
C.9
D.10
Explanation
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.
💡 Practice unlimited CDS PYQs + AI-tracked progress on each topic. Sign up free →