Question

Verify the identity sec(theta)sin(theta)cot(theta) = 1

Answer 1

secant = hypotenuse / adjacent
sine = opposite / hypotenuse
cotangent = adjacent / opposite

So, if we multiply all three we have a numerator of
hypotenuse * opposite * adjacent and a denominator of
adjacent * hypotenuse * opposite

Notice that "hypotenuse", "opposite", and "adjacent" appear exactly once in the numerator AND the denominator.

When numerator = denominator, then a fraction equals ONE.