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Question #cc4ce

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Mar 22, 2017

$LHS= (sina+sinb-sin(a+b)) / (sina+sinb+sin(a+b) )$

$=(2sin((a+b)/2)cos((a-b)/2)-2sin((a+b)/2)cos((a+b)/2) )/(2sin((a+b)/2)cos((a-b)/2)+2sin((a+b)/2)cos((a+b)/2) )$

$=(2sin((a+b)/2)(cos((a-b)/2)-cos((a+b)/2)) )/(2sin((a+b)/2)(cos((a-b)/2)+cos((a+b)/2) ))$

$=(cos((a-b)/2)-cos((a+b)/2)) /(cos((a-b)/2)+cos((a+b)/2) )$

$=(2sin(a/2)sin(b/2)) /(2cos(a/2)cos(b/2))$

$= tan(a/2)tan(b/2) =RHS$

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