Hi Tracy -- I attended Horseheads High school and will be visiting the area in coming weeks.
Sometimes it's helpful simply to plug in directly the triangle sides in each of these ratios:
secx=hyp/adj, tanx=opp/a, sinx=opp/h
h/a - opp/a(opp/h)= a/h ==> a*a/h= h*h/h - opp*opp/h :
factor out 1/h ==> a*a= h*h - opp*opp which is the <a^2 + b^2 = c^2> identity.
Any trig identity with the sides actually plugged in should land here ... Regards & send me an Email :)