Correct Answer - Option 1 : [3, 4]
Concept:
-1 ≤ sin x ≤ 1
0 ≤ sin2 x ≤ 1
Calculation:
Given:
f(x) = 3 sin2 x + 4 cos2 x
= 3 sin2 x + 3 cos2 x + cos2 x
= cos2 x + 3 (sin2 x + cos2 x)
= cos2 x + 3 (∵sin2 x + cos2 x = 1)
As we know that, 0 ≤ cos2 x ≤ 1
⇒ 3 + 0 ≤ 3 + cos2 x ≤ 3 + 1
⇒ 3 ≤ f(x) ≤ 4
∴ Range of the f(x) is [3, 4]
