Trig identities math problem?

Question

2sinxcosy=sin(x+y) + sin(x-y)

Answer 1

Start with the RHS and use the expansions
sin(x+y) = sinxcosy+cosxsiny
sin(x-y) = sinxcosy-cosxsiny

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Answer 2

are you trying to verify the identity?

RHS:
sin (x + y) = sin x cos y + sin y cos x
sin (x - y) = sin x cos y - sin y cos x

adding: sin (x + y) + sin (x - y) = sin x cos y + sin y cos x + sinn x cos y - sin y cos x = 2 sin x cos y = LHS QED

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