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Find the fundamental period of f(x)=cosx...

Find the fundamental period of `f(x)=cosxcos2xcos3xdot`

Text Solution

Verified by Experts

The correct Answer is:
`pi`
`f(x)=cosx cos2x cos 3x`
`cosx,cos2x,` and `cos 3x` are periodic with period `2pi,pi,` and `(2pi)/(3)`
L.C.M. of `(pi,2pi, (2pi)/(3))=2pi`
But `f(x+pi)=cos(x+pi) cos(2x+2pi)cos(3x+3pi)`
`=(-cosx)(cos 2x)(-cos 3x)`
`=cosx cos 2x cos 3x`
`=f(x)`
Hence, period is `pi`.
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