CDS 2024 · PYQ · Trigonometry · easy
What is the difference between the greatest value and the least value of cos²θ + 3 sin²θ + 2 ?
Answer
The correct answer is C: 2. cos²θ + 3sin²θ + 2 = cos²θ + sin²θ + 2sin²θ + 2 = 1 + 2sin²θ + 2 = 3 + 2sin²θ. Since sin²θ ranges from 0 to 1, the expression ranges from 3 to 5.
- A.4
- B.3
- C.2✓ Correct
- D.1
cos²θ + 3sin²θ + 2 = cos²θ + sin²θ + 2sin²θ + 2 = 1 + 2sin²θ + 2 = 3 + 2sin²θ. Since sin²θ ranges from 0 to 1, the expression ranges from 3 to 5. Difference = 5 − 3 = 2.
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