$3 {sin}^{2} x - 4 {cos}^{2} x \in$

[0, 3]

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[- 4, 0]

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[- 3, 4]

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[- 4, 3]

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Solution

The correct option is B $[- 4, 3]$
Let $f (x) = 3 {sin}^{2} x - 4 {cos}^{2} x$
$= 3 ({sin}^{2} x + {cos}^{2} x) - 7 {cos}^{2} x$
$f (x) = 3 - 7 {cos}^{2} x$
max. value of $f (x) = 3$ when, $cos x = 0$
min. value of $f (x) = 3 - 7 = - 4$ , when, $cos x = 1$
range of $f (x) \in [- 4, 3] .$

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