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Math Help - Proving of trigonometric summation

  1. #1
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    Proving of trigonometric summation

    Good Day,

    I need help to prove the following

    sin x + sin 2x + sin 3x + ... + sin nx = {sin (n/2)x sin [(n+1)/2]x}/ sin (x/2)

    Can it be proved without using induction?
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  2. #2
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    Re: Proving of trigonometric summation

    Quote Originally Posted by dd86 View Post
    Good Day,

    I need help to prove the following

    sin x + sin 2x + sin 3x + ... + sin nx = {sin (n/2)x sin [(n+1)/2]x}/ sin (x/2)

    Can it be proved without using induction?
    Why don't you want to try induction?
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  3. #3
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    Re: Proving of trigonometric summation

    I was just wondering if it could be done without using induction, that's why...
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  4. #4
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    Re: Proving of trigonometric summation

    Good Day,

    I've tried many things to help prove the above summation. However, I don't seem to be getting anywhere.

    I've attached a copy of my most logical steps to prove the above summation. Whatever I've done from that point onwards i.e. applying addition and product to sum or sum to product formulas were not included as they were only rough workings.

    Proving of trigonometric summation-img.jpg

    I really hope some one can point me in the right direction to help me prove this.
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