Question

If cos (A + B) =4/5 and sin(A – B) =5/13
where a lie between 0 and, then
find that value of tan2A​

Answer 1

Answer:

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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