The minimum value of $4 {cos}^{2} x + 5 {sin}^{2} x$ is

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Solution

Let
$= 4 (1 - s i n^{2} x) + 5 s i n^{2} x$
$= 4 + s i n^{2} x$
Since minimum value of $s i n^{2} x = 0$
so minimum value $= 4$

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