The maximum value of 4sin^2 x + 3cos^2 x is | vedclass

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(B) Let $f(x) = 4\sin^2 x + 3\cos^2 x$.Using the identity $\sin^2 x + \cos^2 x = 1$,we can write $\cos^2 x = 1 - \sin^2 x$.Substituting this into the

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$4$

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(B) Let $f(x) = 4\sin^2 x + 3\cos^2 x$.Using the identity $\sin^2 x + \cos^2 x = 1$,we can write $\cos^2 x = 1 - \sin^2 x$.Substituting this into the expression: $f(x) = 4\sin^2 x + 3(1 - \sin^2 x)$.$f(x) = 4\sin^2 x + 3 - 3\sin^2 x$.$f(x) = \sin^2 x + 3$.Since the range of $\sin x$ is $[-1, 1]$,the range of $\sin^2 x$ is $[0, 1]$.To find the maximum value,we take the maximum value of $\sin^2 x$,which is $1$.Maximum value $= 1 + 3 = 4$.

The maximum value of $4\sin^2 x + 3\cos^2 x$ is

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