Let f(x) = sin x and g(x) = cos x. Which of t | vedclass

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(C) Given $f(x) = \sin x$ and $g(x) = \cos x$.$1$. For $f(g(x)) = \sin(\cos x)$:Since $\cos(x + 2\pi) = \cos x$,the period is $2\pi$. Thus,statement $

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$f(g(x))$ is an odd function.

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(C) Given $f(x) = \sin x$ and $g(x) = \cos x$.$1$. For $f(g(x)) = \sin(\cos x)$:Since $\cos(x + 2\pi) = \cos x$,the period is $2\pi$. Thus,statement $A$ is true.$2$. For $g(f(x)) = \cos(\sin x)$:Since $\sin(x + \pi) = -\sin x$ and $\cos(-	heta) = \cos 	heta$,we have $\cos(\sin(x + \pi)) = \cos(-\sin x) = \cos(\sin x)$. The period is $\pi$. Thus,statement $B$ is true.$3$. Checking parity of $f(g(x))$:$f(g(-x)) = \sin(\cos(-x)) = \sin(\cos x) = f(g(x))$.Since $f(g(-x)) = f(g(x))$,$f(g(x))$ is an even function. Therefore,statement $C$ is false.$4$. Checking parity of $g(f(x))$:$g(f(-x)) = \cos(\sin(-x)) = \cos(-\sin x) = \cos(\sin x) = g(f(x))$.Since $g(f(-x)) = g(f(x))$,$g(f(x))$ is an even function. Therefore,statement $D$ is true.Conclusion: Statement $C$ is the false statement.

Let $f(x) = \sin x$ and $g(x) = \cos x$. Which of the following statements is false?

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