# Find period of function f(x)=3 sin (pix/3)+4cos (pix/4)

Solution:  We have ,

$f(x)= 3 \sin \frac{\pi x}{3}+4 \cos \frac{\pi x}{4}$

$\\ \\ \Rightarrow \hspace{1cm}T_{1}=\frac{2\pi}{\frac{\pi}{3}}=\frac{6}{1}\hspace{0.5cm}and \hspace{0.5cm}T_{2}=\frac{2\pi}{\frac{\pi}{4}}=\frac{8}{1}\\ \\ \Rightarrow \hspace{1cm}T=(\frac{LCM\hspace{0.2cm} of\hspace{0.2cm}6,8 }{HCF \hspace{0.2cm} of \hspace{0.2cm} 1,1})=24$

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