Sin3x/2 * Cosx/2 - cos3x/2 * sinx/2=0 sin3x - sinX * cos2x=0

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вопрос

To simplify the given expression, we first need to apply trigonometric identities.

Using the double angle identity, cos(2x) = 1 - 2sin^2(x).

Using the half-angle identities, sin(x/2) = ±√((1 - cos(x))/2) and cos(x/2) = ±√((1 + cos(x))/2).

Now we can substitute these identities into the expression sin(3x) - sin(x) * cos(2x):

sin(3x) - sin(x) * (1 - 2sin^2(x))
= sin(3x) - sin(x) + 2sin^3(x)
= sin(3x) - sin(x) + 2sin(x)(1 - cos^2(x))
= sin(3x) - sin(x) + 2sin(x) - 2sin^3(x)
= sin(3x) - sin(x) + 2sin(x) - 2sin(3x)
= -sin(x) + 2sin(x)
= sin(x).

Therefore, the simplified expression is sin(x).