Question

tan (A+B) =1/2 and tan(A-B) = 1/3 then find the value of tan (2A) and tan(2B).

Answer 1

tan 2A = tan ( (A + B) + (A -B) )
= ( tan ( A+ B ) + tan (A - B))  / 1 -tan ( A+ B ) tan (A - B)
= (m + n) / 1 - mn 
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tan 2B = tan ( (A + B) - (A -B) )
= ( tan ( A+ B ) - tan (A - B)) /1 + tan ( A+ B ) tan (A - B)
= (m - n) / 1 + mn