Our teacher gave the class a challenge problem.
If z = tan(A/2), show that cos(A) = (1 - z^2)/(1 + z^2)
I know that replacing z^2 with tan(A/2) is a start but have no idea where to go from there.
Hope you know the identity
cos2A=(cosA)^2-(sinA)^2 which is equal to
but (cosA)^2+(sinA)^2=1 therfor
now dividing both numerator and denominator by (cosA)^2
now put A/2 in place of A and you get
but tanA/2=z therfor