The period of the function f(x) = frac{2 sin | vedclass

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(A) To find the period of $f(x)$,we find the periods of the individual trigonometric functions in the numerator and denominator.Numerator: $2 \sin \le

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$30$

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(A) To find the period of $f(x)$,we find the periods of the individual trigonometric functions in the numerator and denominator.Numerator: $2 \sin \left(\frac{\pi x}{3}ight) \cos \left(\frac{2 \pi x}{5}ight) = \sin \left(\frac{\pi x}{3} + \frac{2 \pi x}{5}ight) + \sin \left(\frac{\pi x}{3} - \frac{2 \pi x}{5}ight) = \sin \left(\frac{11 \pi x}{15}ight) - \sin \left(\frac{\pi x}{15}ight)$.The period of $\sin \left(\frac{11 \pi x}{15}ight)$ is $T_1 = \frac{2 \pi}{11 \pi / 15} = \frac{30}{11}$.The period of $\sin \left(\frac{\pi x}{15}ight)$ is $T_2 = \frac{2 \pi}{\pi / 15} = 30$.The period of the numerator is $	ext{LCM} \left(\frac{30}{11}, 30ight) = \frac{	ext{LCM}(30, 30)}{	ext{HCF}(11, 1)} = 30$.Denominator: The period of $	an \left(\frac{7 \pi x}{2}ight)$ is $T_3 = \frac{\pi}{7 \pi / 2} = \frac{2}{7}$.The period of $\sec \left(\frac{5 \pi x}{3}ight)$ is $T_4 = \frac{2 \pi}{5 \pi / 3} = \frac{6}{5}$.The period of the denominator is $	ext{LCM} \left(\frac{2}{7}, \frac{6}{5}ight) = \frac{	ext{LCM}(2, 6)}{	ext{HCF}(7, 5)} = \frac{6}{1} = 6$.The period of $f(x)$ is $	ext{LCM}(30, 6) = 30$.

The period of the function $f(x) = \frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right) - 5 \sec \left(\frac{5 \pi x}{3}\right)}$ is

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