The minimum value of $5 \sin ^2 \theta+4 \cos ^2 \theta$ is
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The minimum value of $5 \sin ^2 \theta+4 \cos ^2 \theta$ is

(A) 1

(B) 2

(C) 3

(D) 4

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Best answer

SOLUTION — Let

$f(\theta)=5 \sin ^2 \theta+4 \cos ^2 \theta$

$\Rightarrow \quad f(\theta)=\sin ^2 \theta+4$

Since, $\sin ^2 \theta$ lies between 0 and 1 .

$\therefore$ Minimum value of $f(\theta)$ is $0+4=4$

So, The correct option will be (D).

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