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

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(A) To find the period of the function $f(x) = \log(\cos 2x) + \sin 4x$,we analyze the individual components.For the term $\log(\cos 2x)$,the function

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$\pi$

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(A) To find the period of the function $f(x) = \log(\cos 2x) + \sin 4x$,we analyze the individual components.For the term $\log(\cos 2x)$,the function is defined only when $\cos 2x > 0$.The period of $\cos 2x$ is $\frac{2\pi}{2} = \pi$.For the term $\sin 4x$,the period is $\frac{2\pi}{4} = \frac{\pi}{2}$.The period of the sum of two functions is the least common multiple $(LCM)$ of their individual periods.The $LCM$ of $\pi$ and $\frac{\pi}{2}$ is $\pi$.Thus,the period of the function $f(x)$ is $\pi$.

The period of the function $f(x) = \log(\cos 2x) + \sin 4x$ is :-

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