The period of the function f(x) = cos^2(sin x | vedclass

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(C) Given the function $f(x) = \cos^2(\sin x) + \sin^2(\cos x)$.We check for the period $T$ such that $f(x+T) = f(x)$.Let us test $T = \pi$:$f(x + \pi

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$\pi$

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(C) Given the function $f(x) = \cos^2(\sin x) + \sin^2(\cos x)$.We check for the period $T$ such that $f(x+T) = f(x)$.Let us test $T = \pi$:$f(x + \pi) = \cos^2(\sin(x + \pi)) + \sin^2(\cos(x + \pi))$Since $\sin(x + \pi) = -\sin x$ and $\cos(x + \pi) = -\cos x$,we have:$f(x + \pi) = \cos^2(-\sin x) + \sin^2(-\cos x)$Using the properties $\cos(-	heta) = \cos 	heta$ and $\sin(-	heta) = -\sin 	heta$,we get:$f(x + \pi) = \cos^2(\sin x) + (-\sin(\cos x))^2 = \cos^2(\sin x) + \sin^2(\cos x) = f(x)$.Since $f(x + \pi) = f(x)$,the period is $\pi$.

The period of the function $f(x) = \cos^2(\sin x) + \sin^2(\cos x)$ is

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