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Math Help - transformation formulae in trigo

  1. #1
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    Question transformation formulae in trigo

    Any1 plz help me in tis problem:

    if ysinA = xsin(2B + A) then prove that:
    (x+y)cot(A+B) = (y-x)cotB
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  2. #2
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
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    Lightbulb here ir the solution

    Hi!swetabh
    ysinA=xsin(2B+A)
    y/x =sin(2B+A)/sinA
    applying componendo and dividendo we get
    (y+x)/(y-x)=[sin(2B+A)+sinA]/[sin(2B+A)-sinA].............1
    now put sinA =sin(A+B-B) and
    sin(2B+A)=sin[B+(B+A)]in the eq1 and expand them as
    sin(A+B-B)=sin(A+B)cosB-sinBcos(A+B) and
    sin[B+(A+B)]=sinBcos(A+B)+sin(A+B)cosB. By doing this u will finally get
    (y+x)/(y-x)=cotB/cot(A+B)
    now cross multiply and u will get
    (y+x)cot(A+B)=(y-x)cotB
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