If `tan(A+B)=x` and `tan(A-B)=y` then find the values of `tan2A` and `tan2B`

Explanation

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

Now, `tan2A= tan[(A+B)+(A-B)]`

`=(tan(A+B)+tan(A−B))/(1−tan(A+B)×tan(A−B))`

`=(x+y)/(1−xy)`

`tan2A=(x+y)/(1−xy)`

Now, `tan2B= tan[(A+B)-(A-B)]`

`=(tan(A+B)−tan(A−B))/(1+tan(A+B)×tan(A−B))`

`=(x−y)/(1+xy)`

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