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Verified answer
Sin (n + 1)x - sin (n - 1)x= sin (nx + x) - sin(nx - x)
= 2 cos ½ (nx + x + nx - x) sin ½ (nx + x - nx + x)
= 2 cos ½ (2nx) sin ½ (2x)
= 2 cos nx sin x
C