The minimum value of 2 sin²θ+ 3 cos²θis

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The minimum value of 2 sin²θ+ 3 cos²θis

1. 0
2. 3
3. 2
4. 1

Correct Option: C

2 sin²θ + 3cos²θ
= 2 sin²θ + 2cos²θ + cos²θ
= 2 (sin²θ + cos²θ) + cos²θ
= 2 + cos² θ [∵ sin² θ + cos²θ =1]
∵ Minimum value of cos θ = –1
But cos² θ > 0, when θ = 90°
[∵ cos 0° = 1, cos 90° = 0]
∴ Required minimum value = 2 + 0 = 2