Doug C. answered • 12/10/18
Math Tutor with Reputation to make difficult concepts understandable
For a trig identity that looks complicated usually the best strategy is to work on the more complicated side. Since sec2x = tan2x +1 (Pythagorean identity), try substituting that for sec2x on the right hand side. The resulting trinomial in the numerator factors into two binomials. The denominator becomes a difference of squares. After factoring there is a common factor in the numerator and denominator that cancels out, leaving an expression that is identical to the left hand side.
The above strategy also is consistent with the idea of noticing the left hand side consists of all tan. Getting "rid" of the sec functions on the right hand side so that both sides of the identity consist only of tan is likely a step in the right direction (it is as it turns out).
