已知sin(45°+a)sin(45°-a)=-1/4,0°
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已知sin(45°+a)sin(45°-a)=-1/4,0°
![已知sin(45°+a)sin(45°-a)=-1/4,0°](/uploads/image/z/16908316-52-6.jpg?t=%E5%B7%B2%E7%9F%A5sin%EF%BC%8845%C2%B0%2Ba%EF%BC%89sin%EF%BC%8845%C2%B0-a%EF%BC%89%3D-1%2F4%2C0%C2%B0)
1,sin(45+a)sin(45-a)
=sin(45+a)cos(45+a)
=1/2sin(90+2a)
=1/2cos(2a)
=-1/4
解得cos(2a)=-1/2;a=60
2,sin(a+10)(1-(根号3)tan(a-10))
=sin70*(1-(根号3)*tan50)
=cos20/cos50*(cos50-(根号3)*sin50)
=2cos20/sin40*(1/2*cos50-(根号3)/2*sin50)
=1/sin20*sin(30-50)
=1/sin20*(-sin20)
=-1;
=sin(45+a)cos(45+a)
=1/2sin(90+2a)
=1/2cos(2a)
=-1/4
解得cos(2a)=-1/2;a=60
2,sin(a+10)(1-(根号3)tan(a-10))
=sin70*(1-(根号3)*tan50)
=cos20/cos50*(cos50-(根号3)*sin50)
=2cos20/sin40*(1/2*cos50-(根号3)/2*sin50)
=1/sin20*sin(30-50)
=1/sin20*(-sin20)
=-1;
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