Question:
if tan(A B)= x and tan(A-B)= y, find the values of tan 2A and tan 2B
Answer:
Given, tan(A + B) = x and tan(A - B) = y
Now, tan 2A = tan {(A + B) + (A - B)}
=> tan 2A = {tan(A + B) + tan(A - B)}/{1 - tan(A + B) * tan(A - B)}
=> tan 2A = {x + y}/{1 - x * y}
So, tan 2A = (x + y)/(1 - xy)
Again,
Now, tan 2B = tan {(A + B) - (A - B)}
=> tan 2B = {tan(A + B) - tan(A - B)}/{1 + tan(A + B) * tan(A - B)}
=> tan 2B = {x - y}/{1 + x * y}
So, tan 2B = (x - y)/(1 + xy)
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