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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))` |
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Answer» (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)` |
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