Double Angle Formula Proving?

The question is:
Let t=tan(135/2), then use the double angle formula for tan2theta to show that t^2-2t-1=0

1 Answer
May 28, 2018

tan 2 theta = {2 tan theta}/{1 - tan^2 theta }

t = tan (135^circ/2)

tan 135^circ = {2t}/{1-t^2}

-1 = {2t}/{1-t^2}

-1 + t^2 = 2t

t^2 - 2t - 1 = 0 quad sqrt

We can go on and write

t= 1 pm sqrt{2}

135^circ/2 is in the first quadrant so we can choose the positive t for its tangent.