prove identity

Question

Secx-tanxsinx=1/secx

Answer 1

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 :)

Answer 2

secx-tanxsinx

= cosx(sec^2 x - tan^2 x), factor out cosx

= cosx, since sec^2 x - tan^2 x = 1

= 1/secx