Hello,

the confusion is caused by the writing of the fraction:

2/5/2 could be (2/5)/2

or

2/5/2 could be 2/(5/2)

In both cases: You divide by multiplying with the reciprocal. That means:

(2/5)/2 = (2/5) * (1/2) = 1/5

or

2/(5/2) = (2/1) * (2/5) = 4/5

You wrote:

So cot = 1/tan

In turn that means 1/sin/cos

Set paranthese

1/(sin(x)/cos(x)) and multiply with the reciprocal:

(1/1) * (cos(x)/sin(x)) = 1 * cot(x)