The period of sin ^4 x + cos ^4 x is | vedclass

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(D) Let $f(x) = \sin ^4 x + \cos ^4 x$. We can rewrite this using the identity $\sin ^2 x + \cos ^2 x = 1$: $f(x) = (\sin ^2 x + \cos ^2 x)^2 - 2 \sin

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$\frac{\pi}{2}$

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(D) Let $f(x) = \sin ^4 x + \cos ^4 x$. We can rewrite this using the identity $\sin ^2 x + \cos ^2 x = 1$: $f(x) = (\sin ^2 x + \cos ^2 x)^2 - 2 \sin ^2 x \cos ^2 x$ $f(x) = 1 - \frac{1}{2} (2 \sin x \cos x)^2$ $f(x) = 1 - \frac{1}{2} \sin ^2 (2x)$ Using the identity $\sin ^2 	heta = \frac{1 - \cos 2	heta}{2}$: $f(x) = 1 - \frac{1}{2} \left( \frac{1 - \cos 4x}{2} ight)$ $f(x) = 1 - \frac{1}{4} + \frac{\cos 4x}{4} = \frac{3}{4} + \frac{1}{4} \cos 4x$. The period of $\cos(kx)$ is $\frac{2\pi}{|k|}$. Here,$k = 4$,so the period is $\frac{2\pi}{4} = \frac{\pi}{2}$.

The period of $\sin ^4 x + \cos ^4 x$ is

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