tan(a b)=4,cot(a-b)=-3,求tan2a和tan2b

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tan(a b)=4,cot(a-b)=-3,求tan2a和tan2b
tan(a b)=4,cot(a-b)=-3,求tan2a和tan2b

tan(a b)=4,cot(a-b)=-3,求tan2a和tan2b
tan(a+ b)=4,cot(a-b)=-3,→tan(a- b)=-1/3
(1).tan2a=tan[(a+ b)+(a-b)]=
[tan(a+b)+tan(a- b)]/[1-tan(a +b)tan(a- b)]=
[4-1/3]/[1-4*(-1/3)=(11/3)/(7/3)=11/7
(2).tan2b=tan[(a+ b)-(a-b)]=
[tan(a+b)-tan(a- b)]/[1+tan(a +b)tan(a- b)]=
[4-(-1/3)]/[1+4*(-1/3)=(13/3)/(-1/3)=-13