A strange trigonometric identityProving a trigonometric identityWhich trigonometric identities involve trigonometric functions?A trigonometric identityProve this trigonometric identityTrigonometric Identity SymmetryProve $sin^2 theta +cos^4 theta =cos^2 theta +sin^4 theta $How many points to prove a trigonometric identity?What are the practical applications of this trigonometric identity?Help! Cubic trigonometric Identity proofWhat proves this trigonometric identity $cos2 theta=cos^2theta-sin^2theta$?

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A strange trigonometric identity


Proving a trigonometric identityWhich trigonometric identities involve trigonometric functions?A trigonometric identityProve this trigonometric identityTrigonometric Identity SymmetryProve $sin^2 theta +cos^4 theta =cos^2 theta +sin^4 theta $How many points to prove a trigonometric identity?What are the practical applications of this trigonometric identity?Help! Cubic trigonometric Identity proofWhat proves this trigonometric identity $cos2 theta=cos^2theta-sin^2theta$?






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4












$begingroup$


In this paper, equation (4.5), the authors state the trigonometic identity



$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$

Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?










share|cite|improve this question









$endgroup$











  • $begingroup$
    It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
    $endgroup$
    – dbx
    Jun 6 at 13:00

















4












$begingroup$


In this paper, equation (4.5), the authors state the trigonometic identity



$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$

Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?










share|cite|improve this question









$endgroup$











  • $begingroup$
    It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
    $endgroup$
    – dbx
    Jun 6 at 13:00













4












4








4





$begingroup$


In this paper, equation (4.5), the authors state the trigonometic identity



$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$

Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?










share|cite|improve this question









$endgroup$




In this paper, equation (4.5), the authors state the trigonometic identity



$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$

Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?







trigonometry






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jun 6 at 12:53









user14717user14717

3,94011 silver badges20 bronze badges




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  • $begingroup$
    It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
    $endgroup$
    – dbx
    Jun 6 at 13:00
















  • $begingroup$
    It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
    $endgroup$
    – dbx
    Jun 6 at 13:00















$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00




$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00










1 Answer
1






active

oldest

votes


















10












$begingroup$

Hint:



Just write
$$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$



Now, apply the addition formula for $sin(alpha + beta)$.






share|cite|improve this answer









$endgroup$















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    1 Answer
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    active

    oldest

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    10












    $begingroup$

    Hint:



    Just write
    $$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$



    Now, apply the addition formula for $sin(alpha + beta)$.






    share|cite|improve this answer









    $endgroup$

















      10












      $begingroup$

      Hint:



      Just write
      $$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$



      Now, apply the addition formula for $sin(alpha + beta)$.






      share|cite|improve this answer









      $endgroup$















        10












        10








        10





        $begingroup$

        Hint:



        Just write
        $$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$



        Now, apply the addition formula for $sin(alpha + beta)$.






        share|cite|improve this answer









        $endgroup$



        Hint:



        Just write
        $$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$



        Now, apply the addition formula for $sin(alpha + beta)$.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jun 6 at 12:58









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