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Q. If `alpha` is the angle which each side of a regular polygon of `n` sides subtend at...

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user8235304 | Student, Grade 11 | (Level 1) Valedictorian

Posted August 22, 2013 at 5:54 PM via web

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Q. If `alpha` is the angle which each side of a regular polygon of `n` sides subtend at its centre ,then `1+cosalpha + cos2alpha + cos3alpha................` `+cos(n-1)alpha` is equal to:-

A) `n`

B) 0

C) `1`

D)None of these

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aruv | High School Teacher | (Level 2) Valedictorian

Posted August 22, 2013 at 6:41 PM (Answer #1)

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Let

`z=cos(alpha)+isin(alpha)`

`z^2=cos(2alpha)+isin(2alpha)`

`z^(n-1)=cos((n-1)alpha)+isin((n-1)alpha)`

`Thus`

Please correct answer from here

`1+z+z^2+..+z^(n-1)=0`

`1+cos(alpha)+isin(alpha)+cos(2alpha)+sin(2alpha)+....+cos((n-1)alpha)+isin((n-1)alpha)=0`

comparing real and imaginary parts,we have

1+cos(alpha)+cos(2alpha)+...........+cos((n-1)alpha)=0

Thus correct answer is part B instead of D .

correct choice is B

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