2α

\cos 2\alpha=

\sin 2\alpha= 

\tan 2\alpha= 

A = Intersect(xAxis, yAxis)
B = Point(xAxis)
c = Circle(A, B)
C = Point(c)
α = Angle(B, A, C)
a = Segment(A, C)
B' = Rotate(B, 2 * α, A)
β = Angle(B, A, B')
b = Segment(A, B')
sa: y(C)
ca: x(C)
s2a: y(B')
c2a: x(B')
d = Tangent(B, c)
e = Line(A, C)
D = Intersect(e, d)
f = Line(A, B')
F = Intersect(d, f)
h = Segment(B, F)
g = Segment(B, D)
texto4: "" + (LaTeX[c2a]) + ""
texto3: "\cos^2 \alpha - \sin^2 \alpha=(" + (LaTeX[ca]) + ")^2-(" + (LaTeX[sa]) + ")^2="
texto5: "" + (LaTeX[c2a]) + ""
texto1: "2 \sin \alpha \cos \alpha = 2 \times " + (LaTeX[sa]) + " \times " + (LaTeX[ca]) + "="
texto6: "" + (LaTeX[s2a]) + ""
texto7: "" + (LaTeX[s2a]) + ""
ta: y(D)
texto1_3: "\frac{2 \tan \alpha}{1-\tan^2 \alpha}=\frac{2 \times " + (LaTeX[ta]) + "}{1-(" + (LaTeX[ta]) + ")^2}="
t2a: y(F)
texto8: "" + (LaTeX[t2a]) + ""
texto9: "" + (LaTeX[t2a]) + ""
texto10: "α=" + (LaTeX[α]) + ""
texto11: "2\alpha=" + (LaTeX[β]) + ""
i = Line(A, B)
j = OrthogonalLine(A, i)
k = OrthogonalLine(B', j)
l = OrthogonalLine(C, j)
m = OrthogonalLine(B', i)
n = OrthogonalLine(C, i)
E = Intersect(j, k)
G = Intersect(j, l)
H = Intersect(i, m)
I = Intersect(i, n)
p = Segment(E, B')
q = Segment(B', H)
r = Segment(C, I)
s = Segment(C, G)