The maximum of $4 {sin}^{2} x + 3 {cos}^{2} x$ is

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Solution

The correct option is A 4
$4 {sin}^{2} x + 3 {cos}^{2} x = 4 {sin}^{2} x + 3 - 3 {sin}^{2} x = 3 + {sin}^{2} x$
Thus, the maximum value of the expression becomes $4$ since the maximum value of ${sin}^{2} x$ is $1$ .

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