Sin8x*cos5x-cos8x*sin5x=0

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вопрос

To simplify the given expression, we'll use trigonometric identities:

sin(A + B) = sinAcosB + cosAsin
cos(A + B) = cosAcosB - sinAsinB

Let A = 8x and B = 5x:

sin(8x + 5x) = sin8xcos5x + cos8xsin5
cos(8x + 5x) = cos8xcos5x - sin8xsin5x

Expanding the left side of the equations:

sin(13x) = sin8xcos5x + cos8xsin5
cos(13x) = cos8xcos5x - sin8xsin5x

Therefore, sin8xcos5x + cos8xsin5x = sin(13x) = 0

This simplifies the given expression to 0.