If $sinx+siny=sqrt3 (cosy-cosx)$ Find the value of $sin3x+sin3y$ ?

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Answer 1 · 2018-03-25T14:09:49

Given

$sinx+siny=sqrt3 (cosy-cosx)$

$2sin((x+y)/2)cos((x-y)/2)=sqrt3* 2sin((x+y)/2)sin((x-y)/2)$

$=>sin((x+y)/2)cos((x-y)/2)-sqrt3sin((x+y)/2)sin((x-y)/2)=0$

$=>sin((x+y)/2)[cos((x-y)/2)-sqrt3sin((x-y)/2)]=0$

So

$sin((x+y)/2)=0$

$=>(x+y)/2=0$

Now

$sin3x+sin3y$

$=2sin((3(x+y))/2)cos((3(x-y))/2)$

$=2sin(3*0)cos((3(x-y))/2)$

$=0$

If sinx+siny=sqrt3 (cosy-cosx)sinx+siny=sqrt3 (cosy-cosx) Find the value of sin3x+sin3ysin3x+sin3y?