How to prove the identity \sin 2x+\sin 2y=2\sin(x+y)\cos(x−y)

Lainey Goodwin

Lainey Goodwin

Answered question

2022-01-23

How to prove the identity sin2x+sin2y=2sin(x+y)cos(xy)

Answer & Explanation

sphwngzt

sphwngzt

Beginner2022-01-24Added 11 answers

2sin(x+y)cos(xy)=2(sinxcosy+cosxsiny)(cosxcosy+sinxsiny)
=2sinxcosx(cos2y+sin2y)+2sinycosy(cos2x+sin2x)
=2sinxcosx+2sinycosy
=sin2x+sin2y

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