Question

tan (A+B) =x,
tan (A-B) =y
find tan 2A
tan 2B
​

Answer 1

Answer:

Tan2B=(x-y)/(1+xy).

Explanation:

Tan2A=tan[(A+B)+(A-B)]

Expanding using identity of tan

tan2A={tan(A+B)+tan(A-B)}/{1-tan(A+B)tan(A-B)}

Given tan(A+B)=x and tan(A-B)=y

Substituting these values in tan2A expression we get

Tan2A=(x+y)/(1-xy)

Tan2B=tan[(A+B)-(A-B)]

Tan2B=[tan(A+B)-tan(A-B)]/[1+tan(A+B)tan(A-B)]

Resubstituting the values we get

Tan2B=(x-y)/(1+xy).