What is the difference between the greatest value and the least value of cos²θ + 3 sin²θ + 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. Difference = 5 − 3 = 2.