From the Pythagorean Identity
So that means in your example
can someone explain this step? I understand why the secx in the numerator divides with sec^2x to give just secx in the denominator but what does sec^2x or tan^2x translate into that will give the numerator expression of 1+tanx?
(perhaps this should be posted in pre-calc? but it's the end bit of a calculus problem involving taking the derivative of an expression with trig functions)