(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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(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: $f(x) = 4\sin^2 x + 3(1 - \sin^2 x) = 4\sin^2 x + 3 - 3\sin^2 x = \sin^2 x + 3$.Since the range of $\sin^2 x$ is $[0, 1]$,the maximum value of $f(x)$ occurs when $\sin^2 x = 1$.Therefore,the maximum value is $1 + 3 = 4$.