If  tan (A+B)=p,  tan (A−B)=q,tan (𝐴+𝐵)=𝑝,  tan (𝐴−𝐵)=𝑞, then the value of tan2A in terms of p and q is

To find the value of tan2A in terms of p and q, we can use the formula for tan(A+B) and tan(A-B) and the formula for tan2A.

The formula for tan(A+B) is (tanA + tanB) / (1 - tanAtanB) and the formula for tan(A-B) is (tanA - tanB) / (1 + tanAtanB).

Given that tan(A+B) = p and tan(A-B) = q, we can write:

p = (tanA + tanB) / (1 - tanA*tanB) ----(1)

q = (tanA - tanB) / (1 + tanA*tanB) ----(2)

We can solve these two equations to find the values of tanA and tanB.

Next, we use the formula for tan2A, which is 2*tanA / (1 - tan^2A).

Substitute the values of tanA and tanB from equations (1) and (2) into the formula for tan2A to get the value of tan2A in terms of p and q.

After solving these equations, we get:

tan2A = (2*(p+q)) / (1 - p*q)

So, the value of tan2A in terms of p and q is (2*(p+q)) / (1 - p*q).