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The period of f(x)=sin(sin(x)/(5)), is...

The period of `f(x)=sin(sin(x)/(5))`, is

A

`2pi`

B

`2pi//5`

C

`10pi`

D

`5pi`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `f(x)=sin(sin""(x)/(5))" "...(i)`
`:." "f(x+10pi)=sin{sin((x+10pi)/(5))}`
`implies" "f(x+10pi)=sin{sin((x)/(5)+2pi)}`
`implies" "f(x+10pi)=sin{sin((x)/(5))}=f(x)" "["from Eq. (i)"]`
Therefore, the period of f(x) is `10 pi`.
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