If the cotangent and tangent are reciprocals of each other, then what is the cotangent of an angle if the tangent of the same angle is a/b where a and b are not zero?

the answer is

Step-by-step explanation:

First of all, the hypotesis that is very important for the quocient to be well define (remember that we can not dive by zero).

Cotangent and tangent are reciprocals of each other means that one of them is the multiplicative inverse of the other one, i.e. for an angle we have

.

Suppose that your angle is . The hypotesis of the problem says that

.

Using the equation we have

and we are using the hypotesis that because the in the denominator in the last equation.