sin(45+x)sin(45-x)=1/6,x属于(90,180),求sin4x

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sin(45+x)sin(45-x)=1/6,x属于(90,180),求sin4x

sin(45+x)sin(45-x)=1/6,x属于(90,180),求sin4x
sin(45+x)sin(45-x)=1/6,x属于(90,180),求sin4x

sin(45+x)sin(45-x)=1/6,x属于(90,180),求sin4x
2sin(45+x)cos(45+x)=1/3
sin(90+2x)=1/3
cos2x=1/3
sin2x= - 2√2/3
sin4x=2sin2xcos2x=2*1/3*(- 2√2/3)=-4√2/9

sin(45+x)sin[90-(45+x)]=1/6
sin(45+x)cos(45+x)=1/6
2sin(45+x)cos(45+x)=1/3
sin(90+2x)=1/3
cos2x=1/3
sin2x= - 2√2/3
sin4x=2sin2xcos2x=2*1/3*(- 2√2/3)=-4√2/9