If cos(a+b)=4/5, sin(a-b)=5/13 and 0<a,b<pi/4, then tan2a=?

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Solution

given, cos(A+B) = 4/5, thus tan(A+B)=3/4. sin(A-B)=5/13,thus tan(A-B)=5/12. then tan(2A)=tan((A+B)+(A-B)) =(tan(A+B)+tan(A-B))/(1-tan(A+B)tan(A-B)) =(3/4+5/12)/(1-(3/4)(5/12)) =56/33.

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