
已知π/2<b<a<3π/4,cos(a-b)=12/13,sin(a+b)=-3/5,求cos2a
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π<a+b<3π/2,
π/2<a-b<π/4,
所以cos(a+b)=-4/5,sin(a-b)=5/13,
cos2a=cos(a+b+a-b)=cos(a+b)cos(a-b)-sin(a+b)sin(a-b)
=-4/5*12/13-(-3/5)*5/13=-33/65
π/2<a-b<π/4,
所以cos(a+b)=-4/5,sin(a-b)=5/13,
cos2a=cos(a+b+a-b)=cos(a+b)cos(a-b)-sin(a+b)sin(a-b)
=-4/5*12/13-(-3/5)*5/13=-33/65
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