Given thatsin⁡(y−x)cos⁡(x+y)=12sin⁡(x+y)cos⁡(x−y)=13Determiningsin⁡(2x)As stated in my perspective, the question does not make any sense. We know...

Berasiniz1

Berasiniz1

Answered

2022-01-28

Given that 
sin(yx)cos(x+y)=12 
sin(x+y)cos(xy)=13 
Determining sin(2x) 
As stated in my perspective, the question does not make any sense. We know that the double angle identity for sin2x is given by 
sin(2x)=2sincos  
Let us try simpiflying the second equation 
sin(x+y)-cos(x-y)=sinxcosy+cosxsiny-cosxcosy-sinxsiny=cosx(siny-cosy)+sinx(cosy-siny)=(cosx-sinx)(siny-cosy)

Answer & Explanation

Gordon Stephens

Gordon Stephens

Expert

2022-01-29Added 10 answers

Hint
sin2x=sin((x+y)+(xy))=sin(x+y)cos(xy)+cos(x+y)sin(xy)
We know the value of the first summand. For the second use the fact that sine is odd.
(sinx)=sin(x)
so that
sin(yx)=sin(xy)

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