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

TriGonoMetRi

sin a cos b = 1/2 (sin (a + b) + sin (a - b))
cos a sin b = 1/2 (sin (a + b) - sin (a - b))

•••
sin x cos (x+y) - cos x sin (x-y)
= 1/2 (sin (2x + y) + sin (-y)) + 1/2 (sin (2x - y) - sin (-y))
= 1/2 (sin (2x + y) + sin (2x - y))
= 1/2 (2 sin 4x/2 cos 2y/2)
= sin 2x cos y
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