How do prove this to be true?

(secθ/sinθ) - (sinθ/cosθ) = cotθ

Let's fiddle with the left-hand side. Re-write the first term as



Multiply the second term by "1", in the form of and it becomes

Now both terms of the LHS have the same denominator, and can therefore be combined. Next, apply the Pythagorean Identity to the resulting numerator, and take it from there...