Hello there, I have a problem i'm hoping someone can help me with. I'm writing a bit of code for computing the value of pi that converges faster than a previous piece that relies on the leibniz series. Anyway, i'm struggling with showing how this identity arises. tan(2t) = 2 * tan(t) / 1 - tan2(t) So far i've got to this point; sin(2θ) = 2sin(θ)cos(θ) and, cos(2θ) = cos2(θ) - sin2(θ) tan(2θ) = sin(2θ) / cos(2θ) = 2sin(θ) cos(θ) / cos2(θ) - sin2(θ) From there, I know that this is the step i'm supposed to take but i'm struggling to make sense of it. =[ 2sin(θ)cos(θ) / cos2(θ) ] * 1 / 1 - tan2(θ Doing that step brings me back to the identity, but why it works is what I don't understand. I have been told that it is dividing by cos2θ but I must be doing something wrong because it doesn't seem to work out for me. when dividing through by cos2θ I get 2sin(θ)cos(θ) / 1 - tan2θ I would really appreciate someone explaining this without making any large jumps in the reasoning. (I shouldn't be doing maths at this time, but it's really bugging me) Thanks!