cot(x) = sin(x)

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

cos(x) = sin^2(x)

cos(x) = 1 -cos^2(x)

cos^2(x) +cos(x) -1 = 0

By the Quadratic Formula,

cos(x) = {-1 +,-sqrt[1^2 -4(1)(-1)]} / 2(1)

cos(x) = {-1 +,-sqrt(5)}/2

When cos(x) = (1/2)[-1 +sqrt(5)] = 0.618 ----umm, golden ratio conjugate.

angle x then is in the 1st and 4th quadrants.

adjacent side = 0.618

hypotenuse = 1

opposite side = sqrt[1^2 -(0.618)^2] = +,-0.786178

So, cot(x) = adj/opp = 0.618 / (+,-0.786178) = +,-0.786 -------answer.

When cos(x) = (1/2)[-1 -sqrt(5)] = -1.618

Cannot be. The minimum value of the cosine of any angle ios only (-1).

So, reject this factor.