In each of the following cases find the period of the function if it is periodic.
(i) `f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))`

Explanation

(i) Period of `"sin"(pi x)/(sqrt(2))=(2pi)/(pi//sqrt(2))=2 sqrt(2)`
Period of `"cos"(pi x)/(sqrt(3))=(2pi)/(pi//sqrt(3))=2 sqrt(3)`
Now, L.C.M. of two different kinds of irrational number does not exist.
Therefore, f(x) is not periodic.
(ii) Period of `"sin"(pi x)/(sqrt(3))=(2pi)/(pi//sqrt(3))=2 sqrt(3)`
Period of `"cos"(pi x)/(2sqrt(3))=(2pi)/(pi//2sqrt(3))=4 sqrt(3)`
Now, L.C.M. of `(2sqrt(3),4 sqrt(3))`
`=sqrt(3) xx L.C.M. " of " (2,4)=4sqrt(3)`