How do you express cosine in terms of cotangent?

Answer 1

cos(x)=sin(x-tau/4)

tan(x)=sin(x)/cos(x)

sin(x)=tan(x)*cos(x)

cos(x)=tan(x-tau/4)*cos(x-tau/4)

you can see that we have some circular reasoning going on, so the best we can do is express it as a combination of sines and cotangents:

cos(x)=1/cot(x-tau/4)*sin(x-tau/2)

tau=2*pi