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What is the minimum value of 4 sin2 θ + 6 cos2 θ?

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What is the minimum value of 4 sin2 θ + 6 cos2 θ?
1). 4
2). 5
3). 3
4). 1


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Answered by on | Votes 1 |

Formula: sin2 θ + cos2 θ = 1

⇒ Let the minimum value be x.

⇒ x = 4 sin2 θ + 6 cos2 θ

⇒ x = 4 (1 - cos2 θ) + 6 cos2 θ

⇒ x = 4 - 4 cos2 θ + 6 cos2 θ

⇒ x = 4 + 2 cos2 θ

⇒ Value of cos θ is minimum (0) at 90

⇒ x = 4 + 2 × 0

∴ x = 4

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