为什么sin(x+y) - sinx = 2cos(x+y/2)siny/2
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为什么sin(x+y) - sinx = 2cos(x+y/2)siny/2
![为什么sin(x+y) - sinx = 2cos(x+y/2)siny/2](/uploads/image/z/10213936-16-6.jpg?t=%E4%B8%BA%E4%BB%80%E4%B9%88sin%EF%BC%88x%2By%29+-+sinx+%3D+2cos%28x%2By%2F2%29siny%2F2)
x+y=x+y/2+y/2
x=x+y/2-y/2
sin(x+y)=sin(x+y/2+y/2)=sin(x+y/2)cosy/2+cos(x+y/2)siny/2
sinx=sin(x+y/2)cosy/2-cos(x+y/2)siny/2
所以
sin(x+y) - sinx
=sin(x+y/2)cosy/2+cos(x+y/2)siny/2-[sin(x+y/2)cosy/2-cos(x+y/2)siny/2]
= 2cos(x+y/2)siny/2
x=x+y/2-y/2
sin(x+y)=sin(x+y/2+y/2)=sin(x+y/2)cosy/2+cos(x+y/2)siny/2
sinx=sin(x+y/2)cosy/2-cos(x+y/2)siny/2
所以
sin(x+y) - sinx
=sin(x+y/2)cosy/2+cos(x+y/2)siny/2-[sin(x+y/2)cosy/2-cos(x+y/2)siny/2]
= 2cos(x+y/2)siny/2
为什么sin(x+y) - sinx = 2cos(x+y/2)siny/2
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