Prove that $displaystyle sum_r=1^n-1 sin^2 dfracpi rn = dfrac n2$ [closed]

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Prove that $displaystyle sum_r=1^n-1 sin^2 dfracpi rn = dfrac n2$



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closed as off-topic by Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos Aug 30 at 13:03


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Prove that $displaystyle sum_r=1^n-1 sin^2 dfracpi rn = dfrac n2$



Please help me with this I ll be very much grateful






trigonometry







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closed as off-topic by Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos Aug 30 at 13:03


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.












  • The sign for the Euro is not a standard maths notation. Please see math.meta.stackexchange.com/questions/5020/…
    – Lord Shark the Unknown
    Aug 30 at 4:10












up vote
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up vote
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down vote

favorite











Prove that $displaystyle sum_r=1^n-1 sin^2 dfracpi rn = dfrac n2$



Please help me with this I ll be very much grateful






trigonometry







share|cite|improve this question















Prove that $displaystyle sum_r=1^n-1 sin^2 dfracpi rn = dfrac n2$



Please help me with this I ll be very much grateful






trigonometry




trigonometry






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share|cite|improve this question













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edited Aug 30 at 4:35









steven gregory

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asked Aug 30 at 4:07









Abhisek Narayan

1




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closed as off-topic by Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos Aug 30 at 13:03


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos Aug 30 at 13:03


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, max_zorn, Gibbs, Shailesh, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.











  • The sign for the Euro is not a standard maths notation. Please see math.meta.stackexchange.com/questions/5020/…
    – Lord Shark the Unknown
    Aug 30 at 4:10
















  • The sign for the Euro is not a standard maths notation. Please see math.meta.stackexchange.com/questions/5020/…
    – Lord Shark the Unknown
    Aug 30 at 4:10















The sign for the Euro is not a standard maths notation. Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Aug 30 at 4:10




The sign for the Euro is not a standard maths notation. Please see math.meta.stackexchange.com/questions/5020/…
– Lord Shark the Unknown
Aug 30 at 4:10










1 Answer
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Hint:
$$cos 2theta=1-2 sin^2theta$$
$$ sin^2 dfracpi rn = frac1-cos dfrac2pi rn2$$



$$displaystyle sum_r=1^n-1frac1-cos dfrac2pi rn2 $$
$$displaystyle sum_r=1^n-1frac12-frac12sum_r=1^n-1cos dfrac2pi rn $$



Now use this very famous series sum
$$cos(2pi/n)+cos(4pi/n)+cdots+cos(2(n-1)pi/n)=-1,$$






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    1 Answer
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    1 Answer
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    Hint:
    $$cos 2theta=1-2 sin^2theta$$
    $$ sin^2 dfracpi rn = frac1-cos dfrac2pi rn2$$



    $$displaystyle sum_r=1^n-1frac1-cos dfrac2pi rn2 $$
    $$displaystyle sum_r=1^n-1frac12-frac12sum_r=1^n-1cos dfrac2pi rn $$



    Now use this very famous series sum
    $$cos(2pi/n)+cos(4pi/n)+cdots+cos(2(n-1)pi/n)=-1,$$






    share|cite|improve this answer


























      up vote
      1
      down vote













      Hint:
      $$cos 2theta=1-2 sin^2theta$$
      $$ sin^2 dfracpi rn = frac1-cos dfrac2pi rn2$$



      $$displaystyle sum_r=1^n-1frac1-cos dfrac2pi rn2 $$
      $$displaystyle sum_r=1^n-1frac12-frac12sum_r=1^n-1cos dfrac2pi rn $$



      Now use this very famous series sum
      $$cos(2pi/n)+cos(4pi/n)+cdots+cos(2(n-1)pi/n)=-1,$$






      share|cite|improve this answer
























        up vote
        1
        down vote










        up vote
        1
        down vote









        Hint:
        $$cos 2theta=1-2 sin^2theta$$
        $$ sin^2 dfracpi rn = frac1-cos dfrac2pi rn2$$



        $$displaystyle sum_r=1^n-1frac1-cos dfrac2pi rn2 $$
        $$displaystyle sum_r=1^n-1frac12-frac12sum_r=1^n-1cos dfrac2pi rn $$



        Now use this very famous series sum
        $$cos(2pi/n)+cos(4pi/n)+cdots+cos(2(n-1)pi/n)=-1,$$






        share|cite|improve this answer














        Hint:
        $$cos 2theta=1-2 sin^2theta$$
        $$ sin^2 dfracpi rn = frac1-cos dfrac2pi rn2$$



        $$displaystyle sum_r=1^n-1frac1-cos dfrac2pi rn2 $$
        $$displaystyle sum_r=1^n-1frac12-frac12sum_r=1^n-1cos dfrac2pi rn $$



        Now use this very famous series sum
        $$cos(2pi/n)+cos(4pi/n)+cdots+cos(2(n-1)pi/n)=-1,$$







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Aug 30 at 5:07

























        answered Aug 30 at 4:56









        Deepesh Meena

        3,2492824




        3,2492824












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