How does $frac{1-cos x}{1+cos x}$ become $frac{2sin^2(x/2)}{2cos^2(x/2)}$?












-2












$begingroup$


I am new to calculus.



enter image description here



How?



thanks in advance






trigonometry







share|cite|improve this question











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  • $begingroup$
    See sosmath.com/trig/douangl/douangl.html
    $endgroup$
    – Robert Z
    Jan 22 at 12:21






  • 1




    $begingroup$
    The question is unclear, what is it that you want to understand?
    $endgroup$
    – Keen-ameteur
    Jan 22 at 12:21










  • $begingroup$
    Do you understand the previous equation?
    $endgroup$
    – Matti P.
    Jan 22 at 12:25










  • $begingroup$
    yes i dont no how 2 sin got in there
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 12:27






  • 1




    $begingroup$
    thank you , i will study it all :)
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 16:29
















-2












$begingroup$


I am new to calculus.



enter image description here



How?



thanks in advance






trigonometry







share|cite|improve this question











$endgroup$












  • $begingroup$
    See sosmath.com/trig/douangl/douangl.html
    $endgroup$
    – Robert Z
    Jan 22 at 12:21






  • 1




    $begingroup$
    The question is unclear, what is it that you want to understand?
    $endgroup$
    – Keen-ameteur
    Jan 22 at 12:21










  • $begingroup$
    Do you understand the previous equation?
    $endgroup$
    – Matti P.
    Jan 22 at 12:25










  • $begingroup$
    yes i dont no how 2 sin got in there
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 12:27






  • 1




    $begingroup$
    thank you , i will study it all :)
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 16:29














-2












-2








-2





$begingroup$


I am new to calculus.



enter image description here



How?



thanks in advance






trigonometry







share|cite|improve this question











$endgroup$




I am new to calculus.



enter image description here



How?



thanks in advance






trigonometry




trigonometry






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 22 at 15:23









Blue

49k870156




49k870156










asked Jan 22 at 12:19









Sachin RameshSachin Ramesh

61




61












  • $begingroup$
    See sosmath.com/trig/douangl/douangl.html
    $endgroup$
    – Robert Z
    Jan 22 at 12:21






  • 1




    $begingroup$
    The question is unclear, what is it that you want to understand?
    $endgroup$
    – Keen-ameteur
    Jan 22 at 12:21










  • $begingroup$
    Do you understand the previous equation?
    $endgroup$
    – Matti P.
    Jan 22 at 12:25










  • $begingroup$
    yes i dont no how 2 sin got in there
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 12:27






  • 1




    $begingroup$
    thank you , i will study it all :)
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 16:29


















  • $begingroup$
    See sosmath.com/trig/douangl/douangl.html
    $endgroup$
    – Robert Z
    Jan 22 at 12:21






  • 1




    $begingroup$
    The question is unclear, what is it that you want to understand?
    $endgroup$
    – Keen-ameteur
    Jan 22 at 12:21










  • $begingroup$
    Do you understand the previous equation?
    $endgroup$
    – Matti P.
    Jan 22 at 12:25










  • $begingroup$
    yes i dont no how 2 sin got in there
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 12:27






  • 1




    $begingroup$
    thank you , i will study it all :)
    $endgroup$
    – Sachin Ramesh
    Jan 22 at 16:29
















$begingroup$
See sosmath.com/trig/douangl/douangl.html
$endgroup$
– Robert Z
Jan 22 at 12:21




$begingroup$
See sosmath.com/trig/douangl/douangl.html
$endgroup$
– Robert Z
Jan 22 at 12:21




1




1




$begingroup$
The question is unclear, what is it that you want to understand?
$endgroup$
– Keen-ameteur
Jan 22 at 12:21




$begingroup$
The question is unclear, what is it that you want to understand?
$endgroup$
– Keen-ameteur
Jan 22 at 12:21












$begingroup$
Do you understand the previous equation?
$endgroup$
– Matti P.
Jan 22 at 12:25




$begingroup$
Do you understand the previous equation?
$endgroup$
– Matti P.
Jan 22 at 12:25












$begingroup$
yes i dont no how 2 sin got in there
$endgroup$
– Sachin Ramesh
Jan 22 at 12:27




$begingroup$
yes i dont no how 2 sin got in there
$endgroup$
– Sachin Ramesh
Jan 22 at 12:27




1




1




$begingroup$
thank you , i will study it all :)
$endgroup$
– Sachin Ramesh
Jan 22 at 16:29




$begingroup$
thank you , i will study it all :)
$endgroup$
– Sachin Ramesh
Jan 22 at 16:29










2 Answers
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$begingroup$

$1- cos x=1-cos(frac{x}{2}+frac{x}{2})=1-(cos^2(frac{x}{2})-sin^2(frac{x}{2}))=1-(1-sin^2(frac{x}{2}))+sin^2(frac{x}{2})=2 sin^2(frac{x}{2}).$






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$endgroup$





















    0












    $begingroup$

    Use that:



    $$cos(2theta)equiv 1-2sin^2(theta)equiv2cos^2(theta)-1$$






    share|cite|improve this answer









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      2 Answers
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      2 Answers
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      0












      $begingroup$

      $1- cos x=1-cos(frac{x}{2}+frac{x}{2})=1-(cos^2(frac{x}{2})-sin^2(frac{x}{2}))=1-(1-sin^2(frac{x}{2}))+sin^2(frac{x}{2})=2 sin^2(frac{x}{2}).$






      share|cite|improve this answer









      $endgroup$


















        0












        $begingroup$

        $1- cos x=1-cos(frac{x}{2}+frac{x}{2})=1-(cos^2(frac{x}{2})-sin^2(frac{x}{2}))=1-(1-sin^2(frac{x}{2}))+sin^2(frac{x}{2})=2 sin^2(frac{x}{2}).$






        share|cite|improve this answer









        $endgroup$
















          0












          0








          0





          $begingroup$

          $1- cos x=1-cos(frac{x}{2}+frac{x}{2})=1-(cos^2(frac{x}{2})-sin^2(frac{x}{2}))=1-(1-sin^2(frac{x}{2}))+sin^2(frac{x}{2})=2 sin^2(frac{x}{2}).$






          share|cite|improve this answer









          $endgroup$



          $1- cos x=1-cos(frac{x}{2}+frac{x}{2})=1-(cos^2(frac{x}{2})-sin^2(frac{x}{2}))=1-(1-sin^2(frac{x}{2}))+sin^2(frac{x}{2})=2 sin^2(frac{x}{2}).$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 22 at 12:29









          FredFred

          47.8k1849




          47.8k1849























              0












              $begingroup$

              Use that:



              $$cos(2theta)equiv 1-2sin^2(theta)equiv2cos^2(theta)-1$$






              share|cite|improve this answer









              $endgroup$


















                0












                $begingroup$

                Use that:



                $$cos(2theta)equiv 1-2sin^2(theta)equiv2cos^2(theta)-1$$






                share|cite|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  Use that:



                  $$cos(2theta)equiv 1-2sin^2(theta)equiv2cos^2(theta)-1$$






                  share|cite|improve this answer









                  $endgroup$



                  Use that:



                  $$cos(2theta)equiv 1-2sin^2(theta)equiv2cos^2(theta)-1$$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jan 22 at 12:30









                  Rhys HughesRhys Hughes

                  6,9741530




                  6,9741530






























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