First note that this not the graph of y = |cot(x)|.
The equivalent equations for |y| = cot(x) or cot(x) = |y| are
cot(x) = -y or cot(x) = +y
So plot y = cot x and then reflect all the points in the x-axis.
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yes 1 + cot x^2 = csc x^2
d/dt cot (t) dt = - cosec2(t)
Which expression is equivalent to cot t sec t
The derivative of cot(x) is -csc2(x).(Which is the same as -1/sin2(x).)
sec(x)*cot(x) = (1/cos(x))*(cos(x)/sin(x)) = (1/sin(x)) = csc(x)