Question

Verify: sin(x+y)-sin(x-y)=2cosxsiny

Answer 1

Hello,

sin(x+y)=sin x cos y + cos x sin y
sin(x-y)= sin x cos y - cos x sin y
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sin(x+y)-sin(x-y)= 0+2cos x sin y

Answer 2

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

sin(x-y) = sin(x)cos(y) - cos(x)sin(y)

sin(x+y) - sin(x-y) = [sin(x)cos(y) + cos(x)sin(y)] - [sin(x)cos(y) - cos(x)sin(y)]

⇒ sin(x)cos(y) + cos(x)sin(y) - sin(x)cos(y) + cos(x)sin(y)
⇒ sin(x)cos(y) - sin(x)cos(y) + cos(x)sin(y) + cos(x)sin(y)
⇒ 0 + 2cos(x)sin(y)

VERIFIED: sin(x+y)-sin(x-y) = 2cos(x)sin(y)