Differentiation of tan(x) and cotan(x)

The function tan(x) can be written as sin(x)/cos(x), therefore:

If we use the qoutient rule:

If we simplify this:

If we simplify this further:

So the derivative of tan(x) is sec2(x). Now lets try to find the derivative of cotan(x). Finding the derivative of cotan(x) is the same as finding the derivative of cos(x)/sin(x):

If we simplify the above equation:

This gives our answer as:

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