求解sin(x-15)cos(x+15)+cos(x-15)sin(x+15)

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求解sin(x-15)cos(x+15)+cos(x-15)sin(x+15)
求解sin(x-15)cos(x+15)+cos(x-15)sin(x+15)

求解sin(x-15)cos(x+15)+cos(x-15)sin(x+15)
利用公式sin(a+b)=sina cosb + cosa sinb
原式等于sin(x-15+x+15)=sin2x

sin(x-15)cos(x+15)+cos(x-15)sin(x+15)
=sin[(x-15)+(x+15)]
=sin2x

sin(A+B)= sinAcosB + cosAsinB

sin(x-15)cos(x+15)+cos(x-15)sin(x+15)
= sin(x-15+x+15)
=sin(2x)

sin(x-15)cos(x+15)+cos(x-15)sin(x+15)
=sin[(x-15)+(x+15)]
=sin(x-15+x+15)
=sin2x

=sin(x-15+x-15)=sin(2x-30)