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

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(A) Let $f(x) = \sin^4 x + \cos^4 x$. Using the identity $a^2 + b^2 = (a+b)^2 - 2ab$,we have: $f(x) = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x$ $f

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$\pi / 2$

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(A) Let $f(x) = \sin^4 x + \cos^4 x$. Using the identity $a^2 + b^2 = (a+b)^2 - 2ab$,we have: $f(x) = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x$ $f(x) = 1 - 2(\sin x \cos x)^2$ $f(x) = 1 - 2(\frac{\sin 2x}{2})^2$ $f(x) = 1 - \frac{\sin^2 2x}{2}$ Using the identity $\sin^2 	heta = \frac{1 - \cos 2	heta}{2}$: $f(x) = 1 - \frac{1}{2} \left( \frac{1 - \cos 4x}{2} ight)$ $f(x) = 1 - \frac{1}{4} + \frac{1}{4} \cos 4x$ $f(x) = \frac{3}{4} + \frac{1}{4} \cos 4x$ The period of $\cos(kx)$ is $\frac{2\pi}{|k|}$. Therefore,the period of $f(x)$ is $\frac{2\pi}{4} = \frac{\pi}{2}$.

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

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