If $a+b+c=pi$, show $frac{sin a+sin b+sin c}{cos a+cos b+cos...












1















If $a+b+c=pi$ and
$$frac{sin a+sin b+sin c}{cos a+cos b+cos c}=frac{k}{h}$$
then prove that
$$frac{4cos(a/2)cos(b/2)cos(c/2)}{1+4sin(a/2)sin(b/2)sin(c/2)}=frac{k}{h}$$




original problem image



This result is used to solve a problem based on coordinate geometry but I tried wrapping my head around with this.Help please!






geometry trigonometry







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    socratic.org/questions/…
    – lab bhattacharjee
    15 hours ago






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    math.stackexchange.com/questions/176892/…
    – lab bhattacharjee
    15 hours ago










  • thank you lab bhattacharjee
    – ssk
    15 hours ago
















1















If $a+b+c=pi$ and
$$frac{sin a+sin b+sin c}{cos a+cos b+cos c}=frac{k}{h}$$
then prove that
$$frac{4cos(a/2)cos(b/2)cos(c/2)}{1+4sin(a/2)sin(b/2)sin(c/2)}=frac{k}{h}$$




original problem image



This result is used to solve a problem based on coordinate geometry but I tried wrapping my head around with this.Help please!






geometry trigonometry







share|cite|improve this question




















  • 1




    socratic.org/questions/…
    – lab bhattacharjee
    15 hours ago






  • 1




    math.stackexchange.com/questions/176892/…
    – lab bhattacharjee
    15 hours ago










  • thank you lab bhattacharjee
    – ssk
    15 hours ago














1












1








1








If $a+b+c=pi$ and
$$frac{sin a+sin b+sin c}{cos a+cos b+cos c}=frac{k}{h}$$
then prove that
$$frac{4cos(a/2)cos(b/2)cos(c/2)}{1+4sin(a/2)sin(b/2)sin(c/2)}=frac{k}{h}$$




original problem image



This result is used to solve a problem based on coordinate geometry but I tried wrapping my head around with this.Help please!






geometry trigonometry







share|cite|improve this question
















If $a+b+c=pi$ and
$$frac{sin a+sin b+sin c}{cos a+cos b+cos c}=frac{k}{h}$$
then prove that
$$frac{4cos(a/2)cos(b/2)cos(c/2)}{1+4sin(a/2)sin(b/2)sin(c/2)}=frac{k}{h}$$




original problem image



This result is used to solve a problem based on coordinate geometry but I tried wrapping my head around with this.Help please!






geometry trigonometry




geometry trigonometry






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




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edited 15 hours ago









Blue

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asked 15 hours ago









ssk

475




475








  • 1




    socratic.org/questions/…
    – lab bhattacharjee
    15 hours ago






  • 1




    math.stackexchange.com/questions/176892/…
    – lab bhattacharjee
    15 hours ago










  • thank you lab bhattacharjee
    – ssk
    15 hours ago














  • 1




    socratic.org/questions/…
    – lab bhattacharjee
    15 hours ago






  • 1




    math.stackexchange.com/questions/176892/…
    – lab bhattacharjee
    15 hours ago










  • thank you lab bhattacharjee
    – ssk
    15 hours ago








1




1




socratic.org/questions/…
– lab bhattacharjee
15 hours ago




socratic.org/questions/…
– lab bhattacharjee
15 hours ago




1




1




math.stackexchange.com/questions/176892/…
– lab bhattacharjee
15 hours ago




math.stackexchange.com/questions/176892/…
– lab bhattacharjee
15 hours ago












thank you lab bhattacharjee
– ssk
15 hours ago




thank you lab bhattacharjee
– ssk
15 hours ago










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source:– https://socratic.org/questions/if-a-b-c-pi-then-prove-that-sina-sinb-sinc-4cos-a-2-cos-b-2-cos-c-2
suggested by lab bhattacharjee






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    source:– https://socratic.org/questions/if-a-b-c-pi-then-prove-that-sina-sinb-sinc-4cos-a-2-cos-b-2-cos-c-2
    suggested by lab bhattacharjee






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      source:– https://socratic.org/questions/if-a-b-c-pi-then-prove-that-sina-sinb-sinc-4cos-a-2-cos-b-2-cos-c-2
      suggested by lab bhattacharjee






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        source:– https://socratic.org/questions/if-a-b-c-pi-then-prove-that-sina-sinb-sinc-4cos-a-2-cos-b-2-cos-c-2
        suggested by lab bhattacharjee






        share|cite|improve this answer












        source:– https://socratic.org/questions/if-a-b-c-pi-then-prove-that-sina-sinb-sinc-4cos-a-2-cos-b-2-cos-c-2
        suggested by lab bhattacharjee







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        answered 15 hours ago









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