Question

if tan(A+B)=x and tan(A-B)=y find the value of tan 2A and tan2B

Answer 1

we can write 2a= (a+b)+(a-b) and 2b = (a+b)-(a-b)

tan(2a) =tan( (a+b)+(a-b) ) = (tan(a+b) +tan(a-b) ) / ( 1-tan(a+b) tan(a-b)) = (x+y) / (1-xy)

similarly tan(2b) =tan( (a+b)-(a-b) ) = (tan(a+b) - tan(a-b) ) / ( 1+ tan(a+b) tan(a-b)) = (x-y) / (1+xy)

Answer 2

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