Simplify $x^2sinleft(fracx2right)cosleft(fracx2right)$

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In this problem I need to simplify the following expression:



$$x^2sinfracx2cosfracx2$$



However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)







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  • 2




    Use $sin 2x=2sin xcos x$.
    – Lord Shark the Unknown
    Aug 26 at 10:58






  • 2




    $x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
    – Jendrik Stelzner
    Aug 26 at 10:59










  • @amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
    – Pablo
    Aug 26 at 11:00










  • The given expression, a product of algebra and trig, is as simple as it can get.
    – Narasimham
    yesterday











  • this requires you to know $sin(a+b)$
    – Nick
    yesterday














up vote
2
down vote

favorite
1












In this problem I need to simplify the following expression:



$$x^2sinfracx2cosfracx2$$



However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)







share|cite|improve this question


















  • 2




    Use $sin 2x=2sin xcos x$.
    – Lord Shark the Unknown
    Aug 26 at 10:58






  • 2




    $x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
    – Jendrik Stelzner
    Aug 26 at 10:59










  • @amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
    – Pablo
    Aug 26 at 11:00










  • The given expression, a product of algebra and trig, is as simple as it can get.
    – Narasimham
    yesterday











  • this requires you to know $sin(a+b)$
    – Nick
    yesterday












up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





In this problem I need to simplify the following expression:



$$x^2sinfracx2cosfracx2$$



However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)







share|cite|improve this question














In this problem I need to simplify the following expression:



$$x^2sinfracx2cosfracx2$$



However, I can't think of any trigonometric properties or algebraic manipulations that would simplify it. I know this isn't a proper way to ask a question here, without showing any working, but any ideas or hints would be appreciated :)









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited yesterday









Nick

3,61973261




3,61973261










asked Aug 26 at 10:57









Pablo

33312




33312







  • 2




    Use $sin 2x=2sin xcos x$.
    – Lord Shark the Unknown
    Aug 26 at 10:58






  • 2




    $x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
    – Jendrik Stelzner
    Aug 26 at 10:59










  • @amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
    – Pablo
    Aug 26 at 11:00










  • The given expression, a product of algebra and trig, is as simple as it can get.
    – Narasimham
    yesterday











  • this requires you to know $sin(a+b)$
    – Nick
    yesterday












  • 2




    Use $sin 2x=2sin xcos x$.
    – Lord Shark the Unknown
    Aug 26 at 10:58






  • 2




    $x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
    – Jendrik Stelzner
    Aug 26 at 10:59










  • @amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
    – Pablo
    Aug 26 at 11:00










  • The given expression, a product of algebra and trig, is as simple as it can get.
    – Narasimham
    yesterday











  • this requires you to know $sin(a+b)$
    – Nick
    yesterday







2




2




Use $sin 2x=2sin xcos x$.
– Lord Shark the Unknown
Aug 26 at 10:58




Use $sin 2x=2sin xcos x$.
– Lord Shark the Unknown
Aug 26 at 10:58




2




2




$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
– Jendrik Stelzner
Aug 26 at 10:59




$x^2 sin fracx2 cos fracx2$ is not an equation. Do you want to simplify this expression?
– Jendrik Stelzner
Aug 26 at 10:59












@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
– Pablo
Aug 26 at 11:00




@amsmathim guessing thats the fully simplified equation, but im interested in knowing how to simplify it, rather than just knowing the answer
– Pablo
Aug 26 at 11:00












The given expression, a product of algebra and trig, is as simple as it can get.
– Narasimham
yesterday





The given expression, a product of algebra and trig, is as simple as it can get.
– Narasimham
yesterday













this requires you to know $sin(a+b)$
– Nick
yesterday




this requires you to know $sin(a+b)$
– Nick
yesterday










2 Answers
2






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up vote
6
down vote



accepted










Recall that



$$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$



therefore with $theta=frac x 2$ we have



$$x^2sinfracx2cosfracx2=frac12x^2sin x$$






share|cite|improve this answer



























    up vote
    1
    down vote













    $$ sin x = 2 sin (x/2) cos (x/2) $$



    Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$



    No more simplification is possible.






    share|cite|improve this answer




















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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      6
      down vote



      accepted










      Recall that



      $$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$



      therefore with $theta=frac x 2$ we have



      $$x^2sinfracx2cosfracx2=frac12x^2sin x$$






      share|cite|improve this answer
























        up vote
        6
        down vote



        accepted










        Recall that



        $$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$



        therefore with $theta=frac x 2$ we have



        $$x^2sinfracx2cosfracx2=frac12x^2sin x$$






        share|cite|improve this answer






















          up vote
          6
          down vote



          accepted







          up vote
          6
          down vote



          accepted






          Recall that



          $$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$



          therefore with $theta=frac x 2$ we have



          $$x^2sinfracx2cosfracx2=frac12x^2sin x$$






          share|cite|improve this answer












          Recall that



          $$sin 2theta =2sin theta cos theta implies sin theta cos theta=frac12sin 2theta $$



          therefore with $theta=frac x 2$ we have



          $$x^2sinfracx2cosfracx2=frac12x^2sin x$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 26 at 10:59









          gimusi

          70.1k73786




          70.1k73786




















              up vote
              1
              down vote













              $$ sin x = 2 sin (x/2) cos (x/2) $$



              Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$



              No more simplification is possible.






              share|cite|improve this answer
























                up vote
                1
                down vote













                $$ sin x = 2 sin (x/2) cos (x/2) $$



                Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$



                No more simplification is possible.






                share|cite|improve this answer






















                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  $$ sin x = 2 sin (x/2) cos (x/2) $$



                  Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$



                  No more simplification is possible.






                  share|cite|improve this answer












                  $$ sin x = 2 sin (x/2) cos (x/2) $$



                  Thus we have $$ x^2sinfracx2cosfracx2=frac12x^2sin x$$



                  No more simplification is possible.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Aug 26 at 11:07









                  Mohammad Riazi-Kermani

                  30.5k41852




                  30.5k41852



























                       

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