From tan (2A) = 2tanA/(1 - tan^2 A) we get
tanx = 2tan(1/2 x)/(1 - tan^2 (1/2 x))
= 2b/(1-b^2)
If tan(1/2 x)=b express tanx in terms of b
2 answers
tan(1/2 x) = b
We know that
tan(A + B) = (tanA + tanB)/(1 - tanAtanB)
so
tanx = tan(1/2 x + 1/2 x) =
[tan(1/2 x) + tan(1/2 x) ] / 1 - ( tan(1/2 x)tan(1/2 x) )
= (b + b) / 1 - (bxb)
= 2b / (1 - b²)
We know that
tan(A + B) = (tanA + tanB)/(1 - tanAtanB)
so
tanx = tan(1/2 x + 1/2 x) =
[tan(1/2 x) + tan(1/2 x) ] / 1 - ( tan(1/2 x)tan(1/2 x) )
= (b + b) / 1 - (bxb)
= 2b / (1 - b²)