The given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
The identity is
sin(x+ y) - sin (x- y) = 2 cos x sin y
Here we have to use the trigonometric function
Consider the right hand side of the equation
We know
sin (x+ y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y
Then
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
Eliminate the terms
= cos x sin y + cos x sin y
= 2 cos x sin y
Hence, the given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
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