sinx*sin(x+y)+cosx*cos(x+y)等于?

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sinx*sin(x+y)+cosx*cos(x+y)等于?

sinx*sin(x+y)+cosx*cos(x+y)等于?
sinx*sin(x+y)+cosx*cos(x+y)等于?

sinx*sin(x+y)+cosx*cos(x+y)等于?
∵cos(A-B)=cosA*cosB+sinA*sinB
∴逆用以上公式得
sinx*sin(x+y)+cosx*cos(x+y)
=cos[(x+y)-x]
=cosy
∴sinx*sin(x+y)+cosx*cos(x+y)=cosy

cosy
是公式
cosa*cosb+sina*sinb=cos(a-b)

cosy

sinx*sin(x+y)+cosx*cos(x+y)=cos(x+y-x)=cosy
因为sina*sinb+cosa*cosb=cos(b-a)

由公式cos(A-B)=cosA*cosB+sinA*sinB

sinx*sin(x+y)+cosx*cos(x+y)
=cosx*cos(x+y)+sinx*sin(x+y)【注意变化】
=cos[(x+y)-x]
=cosy
∴sinx*sin(x+y)+cosx*cos(x+y)=cosy

cosy
是公式
cosa*cosb+sina*sinb=cos(a-b)
∵cos(A-B)=cosA*cosB+sinA*sinB
∴逆用以上公式得
sinx*sin(x+y)+cosx*cos(x+y)
=cos[(x+y)-x]
=cosy
∴sinx*sin(x+y)+cosx*cos(x+y)=cosy