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
Question
If
then the value of in terms of and is
Solution
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).
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