The period of the function f(x) = cos 4x + ta | vedclass

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(A) The period of $\cos(ax)$ is $\frac{2\pi}{|a|}$. Thus,the period of $\cos 4x$ is $T_1 = \frac{2\pi}{4} = \frac{\pi}{2}$.The period of $	an(bx)$ is

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$\pi$

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(A) The period of $\cos(ax)$ is $\frac{2\pi}{|a|}$. Thus,the period of $\cos 4x$ is $T_1 = \frac{2\pi}{4} = \frac{\pi}{2}$.The period of $	an(bx)$ is $\frac{\pi}{|b|}$. Thus,the period of $	an 3x$ is $T_2 = \frac{\pi}{3}$.The period of the sum of two periodic functions is the least common multiple $(LCM)$ of their individual periods.We need to find $	ext{LCM}\left(\frac{\pi}{2}, \frac{\pi}{3}ight)$.To find the $LCM$ of fractions $\frac{a}{b}$ and $\frac{c}{d}$,we use the formula $\frac{	ext{LCM}(a, c)}{	ext{HCF}(b, d)}$.Here,$	ext{LCM}(\pi, \pi) = \pi$ and $	ext{HCF}(2, 3) = 1$.Therefore,the period is $\frac{\pi}{1} = \pi$.

The period of the function $f(x) = \cos 4x + \tan 3x$ is

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