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Если последняя скобка именно (3х+2), то:
![sin (3x+2y)cos (x+2y)-sin (x+2y)cos (3x+2)=
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frac{1}{2}(sin(3x+2y+x+2y) +sin (3x+2y-x-2y))- \ - frac{1}{2} (sin(x+2y+3x+2)+sin(x+2y-3x-2))
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= frac{1}{2}(sin(4x+4y)+ sin 2x)- frac{1}{2} (sin(4x+2y+2)+sin(2y-2x-2))=
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= frac{1}{2}sin(4x+4y)+ frac{1}{2}sin 2x- frac{1}{2} sin(4x+2y+2)- frac{1}{2}sin(2y-2x-2)](https://tex.z-dn.net/?f=sin+%283x%2B2y%29cos+%28x%2B2y%29-sin+%28x%2B2y%29cos+%283x%2B2%29%3D%0A%5C%0A+frac%7B1%7D%7B2%7D%28sin%283x%2B2y%2Bx%2B2y%29+%2Bsin+%283x%2B2y-x-2y%29%29-+%5C+-+frac%7B1%7D%7B2%7D+%28sin%28x%2B2y%2B3x%2B2%29%2Bsin%28x%2B2y-3x-2%29%29%0A%5C%0A%3D+frac%7B1%7D%7B2%7D%28sin%284x%2B4y%29%2B+sin+2x%29-++frac%7B1%7D%7B2%7D+%28sin%284x%2B2y%2B2%29%2Bsin%282y-2x-2%29%29%3D%0A%5C%0A%3D+frac%7B1%7D%7B2%7Dsin%284x%2B4y%29%2B++frac%7B1%7D%7B2%7Dsin+2x-++frac%7B1%7D%7B2%7D+sin%284x%2B2y%2B2%29-+frac%7B1%7D%7B2%7Dsin%282y-2x-2%29 "sin (3x+2y)cos (x+2y)-sin (x+2y)cos (3x+2)=
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frac{1}{2}(sin(3x+2y+x+2y) +sin (3x+2y-x-2y))- \ - frac{1}{2} (sin(x+2y+3x+2)+sin(x+2y-3x-2))
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= frac{1}{2}(sin(4x+4y)+ sin 2x)- frac{1}{2} (sin(4x+2y+2)+sin(2y-2x-2))=
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= frac{1}{2}sin(4x+4y)+ frac{1}{2}sin 2x- frac{1}{2} sin(4x+2y+2)- frac{1}{2}sin(2y-2x-2)")
Если же последняя скобка должна быть (3х+2у), то:
![sin (3x+2y)cos (x+2y)-sin (x+2y)cos (3x+2y)=
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=sin(3x+2y-x-2y)=sin2x](https://tex.z-dn.net/?f=sin+%283x%2B2y%29cos+%28x%2B2y%29-sin+%28x%2B2y%29cos+%283x%2B2y%29%3D%0A%5C%0A%3Dsin%283x%2B2y-x-2y%29%3Dsin2x "sin (3x+2y)cos (x+2y)-sin (x+2y)cos (3x+2y)=
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=sin(3x+2y-x-2y)=sin2x")
Если же последняя скобка должна быть (3х+2у), то:
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