The period of sin frac{x}{2} - cos frac{x}{3} | vedclass

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(D) The period of $\sin(ax)$ is given by $\frac{2\pi}{|a|}$.For $\sin \frac{x}{2}$, the period is $\frac{2\pi}{1/2} = 4\pi$.For $\cos \frac{x}{3}$, th

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$12$

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(D) The period of $\sin(ax)$ is given by $\frac{2\pi}{|a|}$.For $\sin \frac{x}{2}$, the period is $\frac{2\pi}{1/2} = 4\pi$.For $\cos \frac{x}{3}$, the period is $\frac{2\pi}{1/3} = 6\pi$.The period of the expression $\sin \frac{x}{2} - \cos \frac{x}{3}$ is the least common multiple $(LCM)$ of $4\pi$ and $6\pi$.$LCM(4\pi, 6\pi) = 12\pi$.

The period of $\sin \frac{x}{2} - \cos \frac{x}{3}$ is (in $\pi$)

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