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How demonstrate f(x+3pie)-f(x)=0 when f(x)=ctgx -1?

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greenbel | Honors

Posted August 3, 2013 at 3:08 PM via web

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How demonstrate f(x+3pie)-f(x)=0 when f(x)=ctgx -1?

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aruv | High School Teacher | Valedictorian

Posted August 3, 2013 at 3:20 PM (Answer #1)

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`f(x+3pi)-f(x)=0`

`where`

`f(x)=cot(x)-1`

Ans.

`f(x+3pi)=cot(x+3pi)-1`

Since peridcity of cot(x) is `pi`  

Thus

`cot(x+3pi)=cot(x+2pi+pi)=cot(x+2pi)`

`=cot(x+pi+pi)=cot(x+pi)`

`=cot(x)`

Therefore

`f(x+3pi)=cot(x+3pi)=cot(x)-1`

`therefore`

`f(x+3pi)-f(x)=cot(x)-1-(cot(x)-1)`

`=cot(x)-1-cot(x)+1`

`=0`

Hence proved.

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