Which of the following functions have the max | vedclass

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(D) Let us analyze each function:$1$. For option $A$: $f(x) = \sin^2 x - \cos^2 x = -(\cos^2 x - \sin^2 x) = -\cos 2x$. The range of $\cos 2x$ is $[-1

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All of the above

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(D) Let us analyze each function:$1$. For option $A$: $f(x) = \sin^2 x - \cos^2 x = -(\cos^2 x - \sin^2 x) = -\cos 2x$. The range of $\cos 2x$ is $[-1, 1]$,so the range of $-\cos 2x$ is also $[-1, 1]$. The maximum value is $1$.$2$. For option $B$: $f(x) = \frac{\sin 2x - \cos 2x}{\sqrt{2}} = \frac{1}{\sqrt{2}}\sin 2x - \frac{1}{\sqrt{2}}\cos 2x = \sin(2x - \frac{\pi}{4})$. The range of the sine function is $[-1, 1]$,so the maximum value is $1$.$3$. For option $C$: $f(x) = -\frac{\sin 2x - \cos 2x}{\sqrt{2}} = -\sin(2x - \frac{\pi}{4}) = \sin(\frac{\pi}{4} - 2x)$. The range of the sine function is $[-1, 1]$,so the maximum value is $1$.Since all functions have a maximum value of $1$,the correct option is $D$.

Which of the following functions have the maximum value unity?

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